Pre-heat oven to 350°F.
Cook pasta according to package directions; drain.
Meanwhile, in a large saucepan, heat oil over medium heat.
Add chicken, onion, peppers and seasonings; saute until chicken is no longer pink; add garlic and cook 1 minute longer.
In a blender, pulse tomatoes and tomato paste, covered, until blended; add to chicken mixture.
Stir in broth; bring to a boil over medium-high heat; reduce heat; cover and simmer until slightly thickened, 10 – 15 minutes.
Toss pasta with chicken mixture.
Spoon half of the mixture into a greased 2-quart baking dish.
Sprinkle with half of the cheeses; repeat layers.
Cover with aluminum foil, place in pre-heated oven and bake 30 minutes.
Remove from oven, uncover; bake until heated through; 15 – 20 minutes longer.
