I have a confession to make: I mostly use chicken stock from a box. I buy the organic free range kind, and it's okay, but it's not great. Fine for deglazing a pan, or using as the base of a busy soup, but not something you want to sip hot with just a few slivers of green onion and a slice of ginger.
There aren't many things I miss about working in restaurant kitchens, but chicken stock is one of them. The walk-in always had huge covered buckets of rich, delicious stock, made by someone who wasn't me. They got to deal with roasting pans full of bones and mirepoix, lifting the huge stockpots, simmering, skimming, straining, and reducing gallons of the stuff. I got an unlimited supply of intensely flavorful stock.
In truth, when I do make my own stock, it's usually because when I'm cleaning up after roasting a chicken for dinner, it's easier to scrape the bones and scraps into a freezer bag than it is to take them outside to the green bin. (Our compost bin doesn't get hot enough to handle meat; that goes to the municipal compost facilities.) Sure, the green bin is only ten feet from my back door, but it's cold and dark, and there might be slugs on the ground. So into the freezer it all goes.
Another freezer bag holds mushroom stems, onion ends, carrot peels, leftover bits of herbs and such. They're packed with flavor, but nothing you'd want to chew, so they get simmered with the bones and then strained out. Veggies that are "chew-worthy" go into another bag, to be added to the final soup, perhaps with some noodles or cooked grains. This is what I do with the overripe tomatoes, the last six green beans on the vine, the quarter cup of leftover roasted squash — things that aren't quite enough to do anything with individually, but combine into a nice mixed-veggie soup.
One chicken carcass is not enough to flavor very much stock, so I wait until I have three or four of them. If I don't have enough frozen carcasses, I'll start with an uncooked chicken, or a big package of legs or drumsticks or thighs. If I'm doing it this way, I'll usually pull the chicken out once the meat is falling-off-the-bone tender, fail to let it cool long enough, then pull off the meat and burn my fingers. The bones go back into the pot for a few more hours of simmering.
The meat — minus some of its flavor, but tender, boneless, gently seasoned and already shredded — makes an easy starting point for any number of dishes. Dress it with barbecue sauce and treat it like pulled pork. Make stuffed dumplings, or tamales, or wraps, or chicken salad sandwiches. Or figure out the recipe for La Mediteranée's chicken cilicia — chicken with spices, almonds, raisins, and chickpeas, wrapped in filo and dusted with cinnamon and sugar. Then send it to me.