My favorite way to use all the "unedible" parts of vegetables (stringy stalks, peels, etc) is to make homemade soup stock. It saves me money on buying canned stock or broth, and it uses meat bones and veggie scraps to their fullest.
If I have veggie scraps and no meat bones, I'll stick them in the freezer until I get some bones. And vice versa - if I have bones and no veggies, I'll put the bones in the freezer until all the goodies are there.
When I'm ready, and have a few hours at home, I'll make my pot of stock. First, I put in the veggies...
This time, I had carrot peels, broccoli stems, the core of a bunch of lettuce, and kale stems. Onion peels are great, as well as celery stalks and leaves. Then, I add a couple of bay leaves and peppercorns for extra flavor. I don't add salt because it's easier to cook with if you can salt it to taste later on, according to what you are making.
On top of that, add the meat carcass, if you are making a meat stock. I had frozen innards from 2 organic chickens that hubby smoked on the grill, as well as some of the bones and skin.
Cover it with water, and let it come to a boil on the stove. When it boils, turn the heat to simmer, and let it simmer with a lid on for at least one hour.
Strain the cooled stock to get rid of all the grit, bones, and veggie matter...and you'll have plenty of stock (a few quarts at least) for soups, stews, and other recipes that call for a little broth or stock! This time I also skimmed the fat off the top before storing it, using a ladel. You can freeze it in plastic containers for a long time, or store it in the fridge for 1-2 weeks. I've seen some people freeze it in ice trays and then store them in ziplock bags after they are frozen in cubes. I hope you try this out if you've never done it before!