In a large pot saute the carrots, celery, and onion in olive oil over medium heat for 5 minutes to soften.
Next add in the water, chicken stock, and chicken thighs. Bring to a boil then reduce to a simmer. As the soup cooks, skim off any scum with a large spoon and discard.
Meanwhile, mix together all of the meatball ingredients and form tiny meatballs about a ½ to ¾-inch in diameter. Place the tiny meatballs on a parchment paper lined baking sheet and set aside.
Once the chicken starts to look like it will fall apart (about 40 minutes) remove all the pieces to a cutting board and let cool. Once cool enough to handle, remove the meat and discard the bones, cartilage, and skin. Give the chicken meat a rough chop or shred with a fork.
Place the chicken meat into the simmering soup and continue to cook for another 5 minutes. Taste test the soup and season with salt and pepper to taste.
Meanwhile, bring a large pot of salted water (2 tablespoons kosher salt per gallon of water) to boil. This will be for your pasta.
Drop the meatballs a few at a time into the hot soup and continue to cook at a simmer. The meatballs will cook quickly but can be left simmering while boiling the pasta in the next step.
Cook the pasta in the boiling water until al dente. While pasta is cooking add the parsley to the soup. Strain the pasta into a colander and serve on the side with the soup. Place the pasta into bowls and ladle soup and meatballs into each bowl. Serve with extra grated Pecorino. Enjoy!