For most of my adult life I've been on a quest for chicken soup that tastes like Campbell's Chunky Chicken Noodle, which they made back in the 80's and has, alas, gone the way of the dodo.
This is not that soup. However, it's built on some of the more interesting previous attempts.
The 'dumplings' referred to here are sort of a feather-light steamed biscuit. They are very fluffy, and full of butter and chicken flavor. This is serious comfort food.
Take a smallish stewing chicken (about 2 lbs.) and put in a stockpot. Add enough water to submerge the bottom third, a generous dollop of olive oil, and the juice of one orange. Bring to a boil and simmer, covered, about 90 minutes. You can do this early in the day, then turn it off and leave covered on the stove until dinner-prep time.
Remove chicken from broth. Strain broth if desired and return to pot.
Peel and chop 3 carrots, 3 stalks of celery, 1/2 yellow onion and 1/2 sweet red bell pepper. Add to broth. Throw in about 2 tsps salt, 1/2 tsp pepper, and 1 or 2 teaspoons each: parsley, sage, rosemary and thyme, adjusting the herb quantities to your own taste. Add about a tablespoon of chicken bouillon granules (or 2 cubes).
Strip the chicken meat, chop and return to pot. Cover and let the vegetables simmer about 30 minutes.
Meanwhile, mix the dumplings: Cut 4 tablespoons butter into 1.5 cups Bisquick* mix. It doesn't have to be perfectly blended. It's like making biscuits or pie crust; you want it incorporated but still lumpy. Dribble in milk a tablespoon at a time, stirring after each addition, until you have a shaggy dry dough, like Play-Doh that is nearing the end of its usefulness. (See note at the end.)
Make sure your soup is at a low boil, and there is enough liquid to let the solids swim freely. The dumplings will soak up a lot of liquid and you don't want to run dry. Add water if necessary.
Stir about 2 tablespoons of cornstarch with 1/4 cup of cool water to make a thin gruel. Beat in 1 egg yolk. Beat in about 1/3 cup of heavy cream. Whisk into the hot soup and immediately reduce heat to a low simmer.
Drop golfball-sized forkfulls of dough into the hot broth. (They will float, and expand as they cook.) Simmer uncovered for 20 minutes, then cover tightly and cook for 10 more.
Serve hot in soup plates. Getting the liquid quantities right can be tricky, but the end result should be a thick stew or ragout. This is extremely comforting food, but not too filling if you can manage to control your intake.
*Note: I use Bisquick because it's fast and easy. Any basic biscuit recipe will do, but you'll leave out the acid (lemon juice, vinegar, buttermilk, whatever) and add less milk. Boiled dumplings are perverse: the dryer they go into the pot, the lighter they will cook up. Too much liquid in the batter makes them gluey and heavy.