In a 3-4 quart heavy saucepan, cook yellow peppers, onion, and garlic in 1 tablespoon oil, covered, over moderately low heat, stirring occasionally, until peppers are soft, about 30 minutes.
Stir in cream. In a blender, puree mixture in batches (use caution when blending hot liquids), transferring to a large bowl, and season with salt and pepper. (Sauce may be made 2 days ahead, covered and chilled). Bring sauce to room temperature before proceeding.
In a deep, large heavy skillet, cook mushrooms and peppers in the remaining tablespoon of oil over moderately high heat, stirring occasionally, until peppers are softened, and most of the liquid is evaporated, about 8 minutes, and season with salt and pepper.
Fill a 6-7 quart kettle three fourths full with salted water, and bring to a boil. Stir in ziti, and cook until just tender, about 10 minutes. Reserve 1 cup pasta cooking water, and drain and rinse ziti well in a colander.