Preheat the oven to 375 degrees.
Pre-bake the pie shell. First line the pie shell with parchment paper, or a recycled pie plate works great. Next fill it with dried beans (or baking weights) to keep the shell from puffing while baking.
Bake for 15-20 minutes, then remove the parchment paper and beans. (Save the beans once cooled for future pie crust baking). If the bottom is not fully cooked, return to the oven without the parchment paper for another 5-8 minutes. When finished, remove from the oven and set aside while preparing the filling. Turn the oven temperature down to 350 degrees.
In a large pot sauté the broccoli with a teaspoon of butter or olive oil, cooking until bright in color (5 minutes), then remove from the heat and set aside.
Place the pie crust on a sheet pan. Sprinkle the grated cheese into the pie crust and then the cooked broccoli.
In a large bowl whisk the eggs until smooth. Add the milk, salt, pepper, and scallions and whisk until combined. Pour the mixture into the pie shell, sprinkle with paprika, and carefully place the quiche into the oven.
Bake in the center of the oven for 40 minutes or until solid in the center when gently shaken. Cool on a rack for at least 15 minutes.
Adapted from Mollie Katzen’s Salad People cookbook