Preheat a heavy non-aluminum Dutch oven or similar 6-qt pot over moderately
high heat and add the olive oil. When the oil is fragrant, add the chicken meat
pieces and sauté, turning frequently for 5 or minutes until lightly browned on all
sides. Add the onions and carrots and sauté, stirring constantly, until the onions
are translucent, about 2 minutes. Add the garlic and sauté about 30 seconds. Do
not allow the garlic to brown. Immediately add the broth to the pot. Stir bits and
pieces loose from the bottom of the pot. Add all additional ingredients, lower the
heat to a gently simmer and cover the pot. Simmer gently, stirring occasionally,
until the chicken meat pieces are tender, but not soft, about 5 to 10 minutes. As
the sauce is finishing cooking, add 3 tb oil to a heavy skillet and sauté the bell
peppers, squashes and broccoli over medium heat until just crisp-tender. Add the
veggies to the sauce when the chicken meat is tender, blend all together and turn
off the heat. Adjust the salt, pepper and herb levels to taste. Toss the cooked
pasta with 1 tb oil to prevent sticking and add to the sauce; blend chicken,
veggies and sauce thoroughly and serve along with Parmesan cheese.