Preheat oven to 375 degrees F. In a medium oven-proof nonstick skillet, cook the peppers and onions in olive oil and butter on MEDIUM heat until they are soft, about 4 minutes. Add broccoli and continue to cook for another 4 minutes until broccoli is cooked through. Lightly beat eggs. Add eggs and stir to incorporate. Put pan in oven and bake until the eggs are set, about 6 to 8 minutes. Top with cheese and bake for an additional 2 minutes to melt the cheese. Remove from pan, slice and serve.