Heat oil in 10-inch skillet over medium-high heat. Cook onions and carrots in oil 3 to 4 minutes, stirring frequently, until crisp-tender. Stir in mushrooms and bell peppers.
Spoon vegetables into 4- to 6-quart slow cooker. Stir in remaining ingredients except spaghetti and cheese.
Cover and cook on low heat setting 8 to 10 hours.
Cook and drain spaghetti as directed on package. Serve sauce over spaghetti. Sprinkle with cheese.