I hesitate to write anything, because you have already got two pages of advice from all different perspectives, and the thread won't help if it just causes PFB anxiety!
I agree with your approach that there shouldn't be pudding without tea. That being said, there is no shame in feeding him unsweetened yogurt or fruit as part of his meal. These foods don't need to be treats.
I think there's a real possibility that this isn't about food, though. To me, when a child wakes at 3:30 in the morning, he's probably not managing to sleep through the night because he is overtired. (Sounds strange, perhaps, but it is very common!) You also mentioned he has just dropped his afternoon nap. Would it be worth putting him to bed earlier than usual? I wouldn't hesitate to put him to bed at 5, frankly. At his age he probably needs 12 hours at night, at least, unless he's a superhero. I also think he may be too tired to eat "complicated" foods -- the meals you prepare for the family are probably more varied and less likely to be familiar. Bananas and yogurt require no mental processing on his part because they are things he knows so well.
So, if it were me, I would feed him some yogurt, fruit, milk and put him down early! I think it's likely that the food is not the issue but if you fill him up and he still wakes you'll know for sure.
Also, are you letting him grizzle for a bit? DD often has early morning wakings when she's overtired but often she goes back to sleep if we let her fuss a little. If we go into her room, though, it's too much stimulation and she's absolutely up for the day.
Oh, I see JoInScotland has mentioned the sleep thing already. I agree with the recommendation of HSHC, as long as you don't use it for BF advice! Moving the nap might work as well, but personally I would try an earlier bedtime first.
Good luck.