Preheat the oven to 375°F and coat a 9×13-inch baking dish with non-stick cooking spray.
Heat the oil in a large non-stick skillet over medium heat. Add the peppers and onions; cook, stirring often, until just softened, 4 minutes. Stir in broccoli and 2 tablespoons water, cover and cook 1 minute. Remove the skillet lid and cook until water is fully evaporated, about 1 minute. Transfer mixture to the glass baking dish, spreading it out evenly to cover the bottom.
Whisk the milk, eggs, salt and black pepper together in a medium bowl. Stir in ½ cup cheese. Pour egg mixture over the top and cover with remaining ½ cup cheese.
Bake until edges are set and top is golden, 30 to 35 minutes. Cool in the baking dish on a wire rack for 10 minutes before slicing. Garnish with pico de gallo.
