1 3 1/2–4-lb. chicken
2 carrots, peeled and trimmed
2 ribs celery
2 cups canned whole peeled plum tomatoes
1/2 cup acine de pepe (frog's-eye) or other tiny round pasta
1 bunch escarole, washed and coarsely chopped
1/2 lb. ground beef
1 egg yolk
2 tbsp. dry bread crumbs
1 tbsp. freshly grated parmigiano-reggiano
1 tbsp. freshly grated romano
Leaves from 2 sprigs
1. Put chicken, carrots, celery, tomatoes, 14 cups water, and salt to taste into a large pot. Bring to a boil over high heat, skimming any foam that rises to the surface, then reduce heat to medium-low. Simmer until chicken is just cooked through, about 40 minutes.
2. Meanwhile, cook pasta in a small pot of boiling salted water until just tender, 5–7 minutes. Drain, rinse, and set aside. Put escarole and 2 tbsp. water into a large skillet, cover, cook over medium heat until wilted, 4-5 minutes and set aside. Gently mix ground beef, egg yolk, bread crumbs, cheeses, parsley, garlic, oregano, 1/2 tsp. salt, and 1/4 tsp. pepper together in a large bowl, form into 1/2" meatballs, and set aside.
3. Using a slotted spoon, transfer chicken to a large bowl and set aside to let cool. Strain broth through a cheesecloth-lined colander into a clean medium pot, discarding solids. Shred chicken meat and set aside, discarding skin and bones.
4. Bring broth to a boil over high heat. Add meatballs, reduce heat to medium, and simmer until cooked through, 10-15 minutes. Add shredded chicken, escarole, and pasta and seasonto taste with salt and pepper. Simmer for 15 minutes more.