Preheat your oven to 375°F (190°C) to ensure even baking and a golden top.
Place your prepared pie crust in the 9-inch pie dish. Poke a few holes in the bottom with a fork to prevent bubbling.
Bring water to a boil in a small pot. Blanch the chopped broccoli florets for 2-3 minutes until bright green and tender-crisp. Drain and set aside to cool.
In a skillet over medium heat, sauté the minced garlic in a little olive oil or butter for about 1 minute until fragrant, taking care not to burn it.
In a mixing bowl, whisk together the eggs, milk, dried oregano, salt, and pepper until well combined with no visible egg whites.
Spread the sautéed garlic and blanched broccoli evenly over the bottom of the pie crust. Pour the egg mixture over the broccoli. Sprinkle shredded sharp cheddar cheese generously on top.
Bake the quiche in the preheated oven for 35-40 minutes or until the filling is set and the top is golden brown. A knife inserted in the center should come out clean.
Remove from oven and let cool for about 10 minutes before slicing to allow the filling to set further.