Preheat oven to 350.
Roll pie crust into a pie dish according to package directions. Do not pre-bake.
Pour the broccoli into the pie shell and top with the cheese.
Beat eggs with milk, salt, and pepper. Pour egg mixture over the broccoli and cheese, filling to about ⅔ full.
Bake at 350 for 35-40 minutes or until eggs are set. Allow to cool for 5-10 minutes.