Cook the sausage. Brown the breakfast sausage in a skillet over medium heat, breaking it into crumbles as it cooks. Drain excess grease and remove the sausage from the skillet.
Sauté the vegetables. Add the diced onions and bell peppers to the same skillet. Cook until they begin to soften, then remove from the heat.
Prepare the egg mixture. In a large bowl, combine the eggs, sour cream, salt, and black pepper. Use a hand mixer to blend until smooth.
Assemble the casserole. Lightly grease a 6-quart slow cooker. Add the frozen shredded hash browns, cooked sausage, sautéed vegetables, and shredded cheese. Pour the egg mixture evenly over the ingredients, allowing it to spread throughout the casserole.
Slow cook. Cover and cook on LOW for approximately 6–8 hours, checking toward the earlier end of the cooking window. The casserole is ready when the eggs are set in the center and the internal temperature reaches 165°F.
Rest and serve. Turn off the slow cooker and allow the casserole to rest briefly before serving.