Stuck at 38

Korriban was only the first of several examples I gave.

And yes I did actually do every mission, except (as I said before) the Heroics and Bonus Series.

What would I have to gain by lying about it? That doesn't help the OP in any way.

Not saying you're lying, just that you must have missed some quest chains without knowing it. Your starting planet doesn't have a bonus series so that doesn't really come in to play but it does have some 2+ heroics that can be completed with just you and your companion.
What I was saying about the starting planet is that usually, if you've done every quest (not including heroics) you will be level 10 or 11. This isn't achieved just by sitting grinding enemies either, literally just doing the quests and any of the 'bonus missions' that are incidental to the quest itself (like "kill X enemies"). Because it is the first planet rested xp doesn't usually come in to play either.

So on one character I did leave the starting planet at level 9 but that was because I purposefully ignored some quests, having done that planet before, but every other character (yes, every one) they were level 11 when they left. I can't see that you'd be earning less XP than me, and in fact you'd be earning more if you're taking on orange rated enemies, so there is obviously a disconnect from what you're reporting and what others have witnessed.
The only options I can see are (a) your characters earn less XP than anyone elses or (b) you aren't actually doing every quest. Option (a) seems exceptionally unlikely which only leaves (b), but doesn't mean you are lying.

As plenty of people have pointed out on this thread and many others like it, the only way to fall behind the level curve throughout the game is to skip missions, otherwise you will end up way above the curve. Space Missions, PvP, Flashpoints are not mandatory and you will still be above the curve even if you skip them.

Well my Jugg is 38 just as he should be, on about the 2nd class mission on Hoth, along with whatever bonus quests. If I ever found myself underleveled, I would just PvP and do Space Missions daily until I got to a sufficient level to successfully do my quests. Have you done the extra quests on all the planets so far? Usually doing those puts you in a good place, such as, for example, I got to Taris at 32 ish, did every quest possible EXCEPT heroics with PvP/space missions daily, and got off taris at 36, went to quesh at 36, got off at 37 and am now on Hoth at 38, exactly the level I should be. My suggestion would be to go do some missed quests on previous planets (up to taris, anything lower would be worthless), maybe some bonus series quests, and daily PvP/space missions? Hope that helped!

My Guardian just hit level 41 while doing the Balmorra bonus series. I couldn't find a group for the many, many Heroic 4's on that planet but did the Heroic 2's on my own.
I've now arrived on Quesh and am probably going to just do my class quests because I am so far over-levelled for this stage of the game.

Yes I've done some space missions, PvP, flashpoints and the daily quests associated with them, but I've not sat and ground out XP to get to this point - just played the game.

That's because you skipped content along the way.

It is not possible to be under leveled, just because you don't log off every time to get rested XP. Which was my point. You do not need to have rested XP to stay ahead of the level curb in this game.

Yes it is possible, but only because you miss something somewhere. You do not really need to do anything special to stay ahead of the planets level bracket.

On Typhon my Jedi Knight was lvl 9 when I left. I did every mission on the system other then the heroics. At that point it was my 3rd or 4th run though on Typhon so I knew all the quests.

The amount I was short was so small that doing 4 of the crew skill quests was enough to get me to 10.

On the other hand on Hutta and Ord Mantell on my BH, and Trooper I was lvl 10 without doing the heroics.

My experience:

Commando --
Left Ord Mantell at level 12
Left Coruscant at 18
Did some space missions and generic stuff to hit 20.
Left Taris at 25 (did bonus)
Left Nar Shaddaa at 29 (did bonus at 34 after leaving Tatooine)
Left Tatooine at 34 (did bonus)
Left Alderaan at 37 (xp was really low on this world due to being so high above it -- most missions were gray by 37)
Left Balmorra at 41 (did bonus)
Currently on Quesh, still 41

Vanguard --
Left Ord Mantell at 12
Left Coruscant at 19
Skipped Taris, just did class quests. Left there at 20.
Left Nar Shaddaa at 24
Left Tatooine at 31
Did about half of Alderaan, then blasted the class quests since I'd made it to 35 there and was getting bored.
Did the Quesh planet quests and got to 38.
Went back and just did the Balmorra class quests and made 39.
Did the 1 class quest on Quesh.
Went to Hoth and finished it up at level 43.
Now just landed on Belsavis already 2 levels high and I have skipped 2.5 planets.

Sage --
Left Tython at 11
Left Coruscant at 18
Left Taris at 25
Left Nar Shaddaa at 29
Left Tatooine at 33
Left Alderaan at 38
Just landed on Balmorra

2nd Sage --
Left Tython at 11
Left Coruscant at 19 (did heroic repeats)
Left Taris at 25
Left Nar Shaddaa at 29
Currently on Tatooine at 29. Has completed Anchorhead area, but nothing from the 2nd hub yet.

Shadow --
Left Tython at 11
Left Coruscant at 18
Skipped Taris, except class quests. Left there at 20
Left Nar Shaddaa at 25
Currently on Tatootine, doing bonus quest series. Level 29

Scoundrel --
Left Ord Mantell at 12
Left Coruscant at 19
Dinked around with friends, did a few space missions here and there.
Currently on Taris at 22, still in the 1st section.

Assassin --
Left Korriban at 12
Left Dromund Kaas at 19
Left Balmorra at 25.
Still level 25, hasn't done anything on Nar Shaddaa yet.

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TL;DR -- Every toon I've got is massively over leveled for the planet they're on, with the exception of my Vanguard which skipped 2.5 planets and is therefore only 2 levels above, rather than "massively."

OP at anytime did a 50 drag you through quests? That would explain a cut in experience. I have never been underleveled for any planet and normally just do every quest minus Heroics unless they can be soloed. Just a thought, maybe we aren't getting the whole story?

Nice breakdown.
Yep, that's my experience too. On all characters I've had to skip something to stay within the realms of 'on level'. First character I only did class quests on Alderaan and ignored everything else, second character got to play alderaan so skipped a bunch of Nar Shadaar. My char who has just arrived on Quesh as a lvl 41 did the single class quest and one quest picked up on arrival and has now left the planet. Without the skipping I'd end up doing grey missions, which is also a complaint seen in these forums!
Two completely conflicting reports ("always over level" and "always under level") which can't be reconciled, but I know which version of reality I suffer from!

I guess if the amount of XP to get you to lvl 10 was that small that it simply came down to how many trash mobs you happened to kill while doing your missions. I don't generally go out of my way to kill everything in sight, but equally I don't try and walk around and avoid enemies. If there's a group in my way then I'll take them on. I suppose some people may be trying to avoid fighting as much as possible, which would lead to the situation of being under levelled a little. I suppose if they did that on every planet then maybe that difference gets magnified, but I'm not sure it could be so magnified as reported by the OP!