Preheat oven to 375 degrees F.
Roll out pie crust, if not already shaped, and chill until ready to use.
Place 1-2 cups water in the bottom of a small pot. Add the broccoli,
cover, and bring to a boil. Cook the broccoli until crisp-tender, about
4 minutes. Transfer broccoli to a colander, rinse with cool water, and
drain. Chop broccoli into small pieces.
In a large bowl, whisk together the eggs, milk, salt and pepper. Stir in
the chopped broccoli and cheddar cheese. Pour into the prepared pie
Bake quiche for 35-40 minutes, until eggs are set in the center.
Check on quiche starting at 25 minutes and tent with foil if crust is
browning too quickly.
Let stand for 5 minutes before serving.