I roasted some beets yesterday, with the skins. OMG, I loved them. I cut the beets in quarters, tossed with just enough oil to moisten and then toss with a seasoning mix to coat (dried garlic powder, dill, and Lawry's seasoning salt), and baked for about 45 minutes on 425 (until fork tender).
I didn't mind the skins, but hubby removed his (they slipped off easily, but of course so did the lovely seasoning attached).
I also eat the beet greens when I can get them (a lot of the farmers remove the green tops before bringing to market).
I like the big top leaves of brussels sprout plants too, but they're even harder to find than beet greens.
I like potato skin (best part of the potato I think) and don't even mind sweet potato skin (if it's baked crispy).
I LOVE broccoli stem, cabbage and cauliflower core. Whenever my grandmother cooked any of those veggies, she would cut the head in half and then cut out the core or stem. There'd usually be two pieces and she would give one to my brother and one to me (if my brother didn't want his, she'd eat it. I never refused mine. Even when it comes to healthy, low-calorie foods, I've never been able to say no).
It always seemed like a treat, because there was only one piece for each of us AND we were allowed to salt it ourselves (usually salt on the table was fairly rare).
Another "throw away" I loved was vegetables that were cooked to flavor beef or chicken stock. Grandma would strain the stock. The flavoring veggies (such as celery, onion, cabbage core, carrots, kohlrabi, turnip, rutabaga) left in the sieve would be cooked almost to mush, but grandma and her helpers would eat the soft veggies as we seperated, de-boned and diced the meat. The meat went back into the stock and the soft veggies went into our mouths (along with the occasional piece of meat if we thought we could get away with it - but if you snuck too many, you'd be banished from the helping circle).
The stock-cooked veggies were a "perk" of helping with the soup. If you didn't help, you didn't get any.
when I learned that most professional cooks (on tv, at least) throw away the mushy stock veggies, I was absolutely horrified.
I can't make stock without eating the mushy veggies and thinking of Grandma.
So who else eats the veggie bits many people throw away?