In 12-inch nonstick skillet, cook sausage over medium-high heat 5 to 7 minutes, stirring occasionally, until no longer pink. Add mushrooms and bell peppers; cook 4 to 5 minutes, stirring frequently, until vegetables are tender. Remove mixture from skillet; drain. Wipe skillet clean with paper towel.
In same skillet, melt butter over medium heat. Meanwhile, in large bowl, beat eggs. Stir half-and-half, thyme, salt and pepper into eggs. Add egg mixture to butter in skillet. Cook over medium heat about 7 minutes, stirring constantly, until mixture is firm but still moist. Stir in soup.
Spray 3- to 4-quart slow cooker with cooking spray. In cooker, place half of egg mixture. Top with half each of the sausage mixture and cheese. Repeat layers.
Cover; cook on Low heat setting 30 minutes or until cheese is melted. Mixture can be kept warm on Low heat setting up to 2 hours.