You can easily adapt this recipe to include your favorite vegetables. You could certainly use frozen broccoli in this dish, but I must say, fresh broccoli will provide the best flavor.
Preheat the oven to 350°F.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Add the broccoli and season with 1/4 teaspoon of the salt. Cook until tender and charred in spots, 4 to 5 minutes.
Whisk the eggs, milk, remaining 1 teaspoon salt and black pepper together in a medium bowl until well combined; set aside.
Sprinkle half the cheese over the pie crust. Top with the broccoli, then sprinkle with the remaining cheese. Pour the egg mixture into the crust.
Bake until the edges are set but the center still jiggles just a little, 35 to 40 minutes. Cool for at least 15 minutes.