Preheat your oven to 375 degrees F. Roll your pie dough into a 11-inch circle, then transfer it to a regular 9-inch pie dish. Build up and flute the top edges to create a rim for holding the filling. Line it with aluminum foil. Fill with pie weights or dried beans, then bake for 10 minutes. Remove the dish from the oven, carefully lift out the beans and foil, then return the crust to the oven and bake until light golden, about 3 minutes more. Reduce the oven temperature to 350 degrees F. (At this point, either discard the beans or save them for future pie baking.)

Meanwhile, in a large skillet, heat the oil over medium high. Add the chopped broccoli and cook 4 minutes. Add the green onion and continue cooking until the broccoli is crisp tender and the onion has softened , 1 to 2 minutes more.

In a large mixing bowl, whisk together the eggs, milk, salt, black pepper, and cayenne until well combined.

Scatter the broccoli mixture on the bottom of the blind-baked crust. Sprinkle evenly with the cheddar and half of the Parmesan. Carefully pour in the egg mixture, then sprinkle the remaining Parmesan over the top.

Carefully placed the quiche on a baking sheet to catch any drips. Bake until a knife inserted 1 inch away from the edge of the crust comes out clean and the center is set, about 40 to 50 minutes. If at any point the crust gets darker than you would like, shield it with foil or a pie crust shield. Let rest for 5 to 10 minutes, then slice and serve.