Agree with the previous poster to keep offering. DD ate every veg going till 2, apart from cucumber, pepper or whole tomatoes which she’s never ever accepted (she’s fine with cooked tomatoes in sauces etc). At 2 we started losing the veg she’d accept until we were down to peas (which she’d literally eat frozen and call them lollipop peas so maybe try that?) and corn on the cob like you.
I kept offering/ serving even the ones she’d never accepted, somewhere around 4 cucumber became a firm favourite. Now at 4.5 she’ll even eat the odd cherry tomato occasionally. Pepper still a firm no. But she once again regularly eats broccoli, carrots, cauliflower, sugarsnap peas, butternut squash.
To get the others in/ extras I do do some sneaky hidden ones too.
I make ‘carrot cake’ porridge with grated carrot, courgette and apple then add some raisins, cinnamon and either nut butter or ground almonds.
Also add grated courgette to cheese scones or savoury muffins (and to most things really as it seems to be pretty unnoticeable once cooked).
I do creamy garlic chicken and mushrooms with rice or jacket potatoes - a few of the mushrooms sneak in unnoticed when they’re in the sauce! Similar with adding swede/ turnip, onion and mushrooms to stews which she loves. When the gravy is thick enough she doesn’t seem to mind what’s in it!
Lots of thick veggie soups with lentils added and then blended up - have even managed to hide some red pepper in here!
She loves prawns and noodles so if I chop stir fry veg up small enough I can sneak some of that in too - certainly the bean sprouts, she’s not above picking anything ‘leafy’ she comes across out though!
Already suggested but I do make a tomato sauce with loads of onion, garlic, celery, carrot, courgette etc and then blend it - use this as pizza sauce or for pasta dishes.
Mine also loves olives which although salty I think at least have some other good vitamins in