More fat, more protein... Fat is full fat yoghurt, cheese, cream on sliced up fruit, butter and oil in cooking - a lot of the stuff we are told as adults to do without or avoid or use fat free alternatives, but kids NEED that fat.
You are the one asking for advice and whilst some people have been ... stroppy, shall we say... there is a lot of good advice here, some of which you seem to just discard for no good reason..
For example you said a few pages back something along the lines of 'oh we won't be trying that hummous, we are not a 'dip' family'...
YOU may not like dips - but you've no idea if your child would like hummous, its a good source of protein and fat - but you have entirely discounted it because its not something you eat.
I get the distinct impression that your own diet is pretty limited, and you are not actually entirely aware of which food groups each food falls into.
Bread, pasta, starchy veg like spuds, fruit juices, fruit - these things all break down into or contain a lot of, sugar.
Kids do need some sugar, but when the diet does NOT contain much in the way of real veg (btw, lettuce, cucumber, tomato, all basically = water!) or protein, you will get left with what you currently have, a child whose blood sugar swings around wildly and feels hungry all the time.
Pick a meat he likes - make an omlette with it - call them breakfast pancakes he won't know or if he REALLY will, make him pancakes instead. Put cheese in them as well as meat. Serve with wholegrain toast if you get away wtih the omlette 'con', and a piece of fruit and a full fat yoghurt.
Make him cheese and ham on toast, fruit and yoghurt.
Make him smoothies - fruit, milk, cream even, and hide a handful of oats and some nuts in it. Serve that with toast or cheese on toast.
Batch cook stuff like mild chilli con carne (you can make it REALLY mild), stir in a little full fat yoghurt or cream cheese once its done and serve that over a baked spud, chips or toast for lunch (if you batch cook it, you can portion it out and zap it in the nuke for quick lunches).
Ditto spaghetti bolognese - it takes just a few minutes to cook some pasta and zap some bolognese.
Both those things you can make with beef, or lamb, or both, or a vegetarian alternative, hide TONS of proper veggies in, use oil and butter in the sauce if you like.
Another good batch cook and freeze is roasted med. veg - roast courgette, sweet peppers, cherry tomatoes, carrots etc in some olive oil and some garlic and pepper or whatever you like - bag it up into meal sized portions - reheat and serve it on a baked spud with a lump of cream cheese or a dollop of hummous, on toast ditto, in a pittabread (use the cream cheese or the hummous to glue it in there).
And no he won't end up obese right now whilst you can keep him out of the fridge and the cupboards - but he will find ways of getting food for himself and pretty soon, and if he is still feeling starving all the time and craving sugar/salt filled rubbish because of it, thats when he will get fat.