Step #1 SAUCE-Preheat a heavy non-aluminum Dutch oven or similar 6-qt pot over moderately high heat & add the olive oiil.
Step #2 When the oil is fragrant, add the chicken meat pieces & saute, turning frequently for 5 or mins until lightly browned on all sides.
Step #3 Add the onions & carrots & saute, until the onions are trnaslucent, stirring constantly, about 2 mins.
Step #4 Add the garlic & saute about 30 seconds.
Step #5 Do not allow the garlic to brown.
Step #6 as soon as possible add the broth to the pot.
Step #7 Stir bits & pieces loose from the bottom of the pot.
Step #8 Add all extra ingredients, lower the heat to a carefully simmer and cover the pot.
Step #9 Simmer carefully, until the chicken meat pieces are tender, but not soft, stirring every once in awhile, about 5 to 10 mins.
Step #10 As the sauce is finishing cooking, add 3 tb oil to a heavy skillet & saute the bell peppers, squashes & broccoli over med-heat/flame until just crisp-tender.
Step #11 Add the veggies to the sauce when the chicken meat is tender, mix all together & turn off the heat.
Step #12 Adjust the salt, pepper & herb levels to taste.
Step #13 Toss the cooked pasta with 1 tb oil to prevent sticking & add to the sauce; mix chicken, veggies & sauce thoroughly & serve along with Parmesan cheese.