Bring a large pot of water to a boil; add the broccoli and cook until just tender, about 3 minutes. Drain well.
Preheat the oven to 350°F (180°C). In a large bowl, whisk the eggs, milk, salt, and pepper together in a large bowl. Stir in the broccoli, red pepper, 3/4 -cup (36 ounces) of the Cheddar, and 3 tablespoons (45 ml) of the Parmesan cheese.
Heat the oil in a 12-inch (305 mm) ovenproof nonstick frying pan over medium-high heat. Pour the egg mixture into the pan and reduce the heat to medium. Cook for 3 minutes to set the bottom of the frittata. Sprinkle the top with the remaining 1/4 -cup of the Cheddar (12 ounces) and 1 tablespoon (15 ml) Parmesan cheese.
Transfer the pan to the oven and bake until the frittata is set in the centre and slightly puffy, about 15 minutes.
Let cool for 5 minutes in the pan, and then run a spatula around the edges and slide onto a large plate.