Cook pasta as directed on package; drain and set aside. Meanwhile, sauté mushrooms, peppers and spinach in 1 Tbsp. oil in large skillet until all water has cooked out of mushrooms and spinach. Stir in half the parsley; set aside.
Lightly whisk eggs, pepper and salt in bowl. Stir in cream and 2 oz. cheese. (Do not whip until frothy.)
Heat remaining 2 Tbsp. oil in 10-inch cast iron skillet on medium heat. Add cooked pasta and toss until heated through. Stir in vegetable mixture and 3 oz. cracker pieces. Add egg mixture; let stand undisturbed for 2 min. Use spatula to draw eggs from edge toward center, letting uncooked portion flow to bottom of pan. When eggs have cooked 5 to 7 min. and are still slightly liquid, place skillet in 350°F standard oven.
Bake 10 to 15 min. or until center is still slightly soft. Remove from oven and heat broiler. Sprinkle remaining cheese over frittata. Broil until lightly browned. Sprinkle with remaining parsley and cracker pieces before cutting into 6 wedges.