Cook pasta to al dente; drain, toss with tablespoon of butter and set aside.
To remove skins from tomatoes, blanch tomatoes. To do this, cut a shallow X on the bottom of each tomato. Add to pot of boiling water for one minute; peel skin off.
Chop tomatoes and set aside.
For stock, in heavy bottom, 8-quart pot, brown chicken in olive oil for several minutes. With slotted spoon, remove chicken from pot, and let cool in separate bowl; do not drain drippings from pot.
In pot with drippings, add a little olive oil and sauté onions, carrots, celery for about 5 minutes until slightly tender.
Add the garlic and continue to sauté for another minute or so. Add tomatoes, seasoning, wine and cook for another few minutes. Taste; add more salt and seasoning as desired.
Pour mixture into a heatproof bowl, and set aside.
Fill pot with about 6 quarts of water (or to 3/4 full) and bring to a boil. Peel skin off chicken pieces and add to pot of water. Turn heat down, loosely cover and simmer for about 35 minutes until chicken is fully cooked, making sure to skim off any foam that forms at the top.
While chicken is cooking, make the pesto. To do this, add basil, olive oil, garlic, walnuts to food processor and process until preferred consistency. If too dry, add a little more olive oil.
Stir in grated Pecorino. Store unused pesto in airtight container in refrigerator, or freeze.
Remove chicken when cooked. Let cool to touch and remove meat from bone; discard bones.
If preferred, strain chicken stock to remove any unwanted bits.
Return meat and sautéed veggies to the pot with chicken stock. Season to taste. Once simmering again, add the garbanzo beans and the zucchini and simmer for about wo minutes.
Serve hot, with garnish of grated Parmigiano and chopped parsley.