How to Make It
Preheat the broiler and position a rack 6 inches from the heat. In a 12-inch nonstick ovenproof skillet, cook the bacon over moderately high heat, stirring occasionally, until softened, 3 to 5 minutes. Add the shallots and cook, stirring occasionally, until softened, about 3 minutes. Add the brussels sprouts, season with salt and pepper and cook, tossing occasionally, until crisp-tender and lightly browned, about 5 minutes.
Meanwhile, in a large bowl, beat the eggs with the milk, 1 teaspoon of salt and 1/4 teaspoon of pepper. Stir in the shredded cheese and snipped chives. Pour the egg mixture into the skillet and cook over moderate heat, stirring gently, until the eggs start to set and the bottom is lightly browned, about 5 minutes. Transfer the skillet to the oven and broil the frittata for about 3 minutes, until the center is just set. Run a rubber spatula around the edge of the frittata and slide it onto a serving plate, then cut it into 6 pieces and serve.