Yy to wishing that DC had the same excited interest in veg! 
I give ours fresh veg (and the occasional bit of fruit) twice a day, both morning and evening. They get a bowl of dry pellet food plus a fresh heap of hay in the evenings.
I think the rough guideline is a handful of veg per pig per day but I suspect mine get a bit more than that! They like a variety of stuff - I try to give small amounts of three or four different types of veg each meal, rather than a large portion of one type.
So this morning ours had (we have two boar/ sow pairings so this is a portion split between two pigs)
- two small pieces of cauliflower (they like the florets, stalks and leaves)
- two slices of cucumber
- half a carrot sliced up
- two leaves of romaine lettuce
- two strips of yellow pepper chopped into pieces.
Tonight they'll get a similar amount but some different stuff if possible. Ours also love round lettuce, broccoli (florets or stalks), green and red peppers, celery (including leaves) and small amounts of cabbage or sprout peelings. Spring greens sometimes. Parsley for a treat, or dandelion leaves.
I have tried parsnip and swede which are both fine to give but ours don't like them...likewise they can have fruit in moderation and I've tried grapes, melon and raspberries but ours aren't fussed on any of these. They like the odd bit of green apple and the tops of strawberries but that's about it.
Hope that helps-it's worth experimenting with different types and it's particularly useful if they become partial to stuff you would otherwise put in the food bin! As long as you avoid potato, anything from the onion family (onion, leek or garlic) or iceberg lettuce then most veggie things are fine to give.
Enjoy your pigs, they are fab little creatures 