Heat butter in large nonstick skillet over medium heat until hot. Add broccoli, red pepper and onion, cook 3 to 4 minutes, stirring occasionally. Remove to medium bowl. Add bread and cheese; toss to mix.
Beat eggs, half-and-half, salt and pepper in small bowl until blended. Pour over bread mixture; toss gently to coat. Place about 1/2 cup bread mixture into each muffin cup. Cover and refrigerate 1 hour or overnight.
Make ahead and keep refrigerated for quick weekday morning breakfasts. Reheat in the microwave on HIGH, 2 mini stratas take about 45 seconds.