Preheat oven to 425 degrees.
Steam or microwave your frozen broccoli for 3-5 minutes, drain well, and set aside.
Roll your readymade pie crust and fit it into your pie plate. If you use a frozen readymade shell, you can skip this step.
Bake your empty pie crust in a 425-degree oven for approximately 10 minutes or until lightly golden brown. Remove from oven, lightly brush the pie crust's inside with Dijon mustard, and set aside.
Lower oven to 350 degrees.
Place your drained broccoli into the bottom of the cooked pie shell.
Combine the eggs, salt and pepper, cream, and milk in a mixing bowl. Whisk until well combined. Add the shredded cheese and whisk again.
Pour the mixture over the broccoli into the pie shell. Using a spatula, pat down the cheese and even out the top of the quiche.
Cover the quiche with parchment and bake for 40 minutes. Remove parchment and bake uncovered for another 10 minutes until golden brown and the toothpick inserted into the center comes out clean.
Let quiche rest for 5-10 minutes before slicing and serving.