Preheat oven to 350 degrees F.
Whisk together all of the filling ingredients except for the broccoli, fold that in last.
Pour the filling into a pie crust and place the quiche in the oven on the middle rack.
Bake for 40 - 50 minutes, or until the filling is set. Be sure to check on the quiche at the halfway mark and cover with foil if necessary to prevent the crust from burning.
Allow the quiche to cool slightly, sprinkle with a bit more salt and pepper, and serve warm.