Preheat your oven to 375°F (190°C). This ensures that your quiche will bake evenly and come out perfectly set.
In a pot of boiling water, blanch the chopped broccoli florets for about 2 minutes until they are bright green. Drain and set aside.
In a mixing bowl, whisk together the 4 large eggs and 1 cup of milk until fully combined.
Stir in the minced garlic, dried oregano, salt, and freshly cracked black pepper into the egg mixture.
Add the blanched broccoli and 1 cup of shredded sharp cheddar cheese to the egg mixture. Gently fold everything together.
Pour the broccoli and cheese mixture into the prepared pie crust, spreading it out evenly.
Place the quiche in the preheated oven and bake for 35-40 minutes, or until the top is golden brown and a knife inserted into the center comes out clean.
Once baked, remove the quiche from the oven and let it cool for about 10 minutes before slicing.