Harley's former Mom fed him a nice mix of vegetables every evening, and apparently, he even ate them! But any transition to a new place can change your habits, and that's pretty much happened to Harley. He'll almost always eat peas and apple, and corn, potato, and pears are often accepted. But most other veggies are ignored. Or, more likely, picked up, licked a little, and dropped again.
I think it's because Bruce is so quick to offer him cheese. Because Harley will
always eat cheese, especially if it's a nice, sharp cheddar, and Bruce doesn't want him to starve to death.
Bruce is very weak that way.

But Harley does enjoy tearing up greens, like this leaf of bok choy, and he even eats some while he tears the leaves up into small pieces. He'll also usually eat something if you offer it to him by hand — carrot, zucchini, sunflower sprouts, etc. I think it's part of his Plan For Utter Domination. "If they feed me vegetables, eventually they'll give me more cheese." Something like that. This morning he mostly just licked the apple pieces in his breakfast dish, but he decimated the piece that Bruce held for him.