Preheat oven to 400°F.

Whisk eggs, milk, salt and pepper in a large bowl.

Add broccoli, Cheddar cheese and cayenne pepper to the beaten eggs.

Heat olive oil in a medium ovenproof nonstick skillet over medium high heat.

Add the beaten egg mixture and cook until the edges start to set, about 2 minutes.

Transfer to the oven and bake until the center is set, 15 to 20 minutes.

Let stand for 5 minutes before sliding carefully onto a serving plate and cutting into wedges.