Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking dish with the olive oil. Spread the vegetables in the bottom, then top with a layer of the cheeses, then the ham, and then the scallions.
Whisk together the eggs, milk, salt and red pepper flakes in a medium bowl. Pour the mixture over the layers and bake until lightly golden and the egg is set, about 50 minutes Allow the bake to sit for 5 minutes before cutting and serving.
Recipe courtesy of Giada De Laurentiis