Preheat oven to 350°F. Butter 13x9x2-inch ceramic or glass baking dish. Whisk first 5 ingredients in large bowl; sprinkle generously with pepper. Set aside.
Place sausage in large nonstick skillet; push to 1 side. Add bell pepper to other side of skillet.
Sauté over high heat, breaking up sausage with fork, until sausage is cooked through and bell peppers are brown in spots, about 7 minutes.
Arrange half of bread cubes in prepared dish. Pour half of egg mixture over.
Sprinkle with half of cheese, then half of sausage-pepper mixture. Repeat layering. Let stand 20 minutes or refrigerate overnight, occasionally pressing on bread to submerge.
Bake strata until puffed and brown, about 1 hour. Cool slightly.