Sorry this is so long -- you all inspired me!

I like to roast my veggies, too, but I also roast the bones.
Kids should try this recipe with the help of an adult. It requires lifting a large, very heavy pot full of boiling-hot broth.
When we have a roasted chicken or turkey (whether I make it myself or buy a rotisserie bird at the grocery), I save the carcass after it is stripped of edible meat. Pull off any remaining fat and skin, then put the carcass and any loose bones on a tinfoil-covered cookie sheet. I usually spice it -- a little oregano or marjoram, and lay a few fresh sprigs of rosemary across/inside it -- then spritz liberally with olive oil. (No salt or pepper, though!)
Then I put the whole thing into a low oven (maybe 300-325 Fahrenheit) and roast it for 1.5 - 2 hours, or until it gets browned and smells heavenly. Let it cool slightly, remove the rosemary, then put it and any juices/browned bits on the tinfoil into a ziptop bag and freeze it.
After you collect several of these, you are ready to make some killer stock. This is best done on a weekend or whenever you have a day to spare. The good part is that after you get it going, it doesn't take too much babysitting -- you can be doing other things, so long as you check it once in a while.
Dump frozen carcasses into a large stock pot. 2-4 chicken carcasses, or one turkey carcass.
Add:
- a large unpeeled onion, split in half, that has been studded with maybe 10-15 cloves. (If you have trouble getting the cloves through the peel, you can use a paring knife to make a small starter hole.) Skewer the onion with several toothpicks to help it hold together.
- 1-2 stalks of celery (or your spare celery tops that you've been saving frozen in a ziptop in the freezer)
- a couple of carrots split lengthwise.
- cold water to cover the carcasses by at least 2", if not more. It's really important that you use cold water.
Cover partway (leave the lid cracked slightly to let steam escape) and bring to a simmer (slow bubbles) over low heat. Because you are using cold water, it will take a long time to achieve the simmer, but this way you will be extracting the most flavor.
I let it go for about an hour from when I first put it on the fire, then start skimming off scum and oil about every half hour. I couldn't tell you the total time on the fire... maybe 4 hours, give or take an hour.... but mainly what I'm looking for is color and taste. Over time, the broth darkens somewhat and tastes more intense. Season if you like, but don't add any salt. (You could spoon off a bit into a cup and salt that, if you want to taste it that way.)
Once it tastes like soup to you, set up a large bowl in your sink, with a colander inside it. Ideally the colander should be lined with a couple layers of cheesecloth, but if you don't mind small bits in your broth, you can do without. The bowl should be large enough to catch everything that's in your stock pot.
To help keep splashing down to a minimum, put the pot of soup on a trivet next to your sink, and with tongs or the like, carefully pull out as much of the carcasses as you can, one at a time, and place them in the colander. Then slowly and *carefully* pour the stock through the colander into the bowl.
Rinse out your stockpot. Then carefully lift the colander out of the bowl, let it drain a bit, then set it aside on a plate to catch drips. (Discard the contents of the colander; the drips might be salvagable.)
From here, you can do just about anything. You could refrigerate the stock to let it gel up and remove any remaining fat. You could have some broth straight up! Or, you could put the stock back into the stock pot and go on to make a fantastic soup. Chicken noodle and black bean/lentil are two of my favorites.
Stock freezes well -- you can put it in an icecube tray, then once frozen, shake out the cubes and put them in a ziptop bag.