After a lot of trying, I finally managed to make chicken soup good enough that it didn't make me wish I'd just thrown in a couple of bouillon cubes instead of doing all that work. Here is my recipe.
Bonier parts of one chicken (I used wings, drumsticks, the neck, and the giblets, except for the liver, which John was charitable enough to take off my hands)
Celery, including a few leaves
Water -- should have used more water; although the stock was strong enough, there wasn't much of it
Simmer for 4 hours. By this point it was ten o' clock, so I threw it in the fridge with the idea that I'd do something about it tomorrow.
In the morning it had completely gelled into a firm aspic. This is what a good chicken stock is supposed to do. I was tempted to just eat it as it was, but it wasn't salted at all, and besides, I wanted soup. So I put it back on the stove and melted it again.
I took out all the chicken parts, pulled the meat off and chopped it, and put the meat back in. I chopped up the gizzard very finely, which helps make the chewiness not a problem. (You see I'm not big on giblets.)
Then I had the idea of, instead of throwing the rest of the vegetables in raw and letting them simmer, of sauteing them in olive oil. I believe this was the secret that made it so good. I sauteed onions, carrots, celery, and garlic, just until they were beginning to soften but before the celery lost all its crunch.
Then I threw all the veggies in, added some rice, salt, and pepper, and served it up. It was GOOD. It didn't need seasoning. I was amazed. Then I remembered I had been going to put sour cream in it, so I put a spoonful in my bowl. Then it was even better. And it hadn't even been very hard to make.
Now, however, I am on a celery kick, and want to know what other ways I can cook it to get that yummy taste. Raw, it is so uninspiring to me, but cooked in chicken broth, it becomes exactly what I want. Does anyone have a recipe for celery soup?