Whisk together the eggs, milk, 3/4 teaspoon salt and a few grinds of pepper in a large bowl. Stir in the broccoli, Cheddar and cayenne.
Heat the oil in a medium ovenproof nonstick skillet over medium-high heat. Add the 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 rest for 5 minutes before sliding carefully onto a cutting board. Cut into wedges and transfer to serving plates. Sprinkle with chives. Serve with lettuce leaves and tomato wedges if using.
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