Preheat your oven to 375°F (190°C).
Place the pie crust in a 9-inch dish and prick the bottom with a fork. Pre-bake for 10 minutes.
Melt butter in a skillet over medium heat. Add sliced leeks and sauté until soft, about 5–7 minutes. Let cool slightly.
In a bowl, whisk together eggs, cream, salt, pepper, and nutmeg.
Spread the cooked leeks evenly over the pre-baked crust. Sprinkle grated cheese on top.
Pour the egg and cream mixture over the leeks and cheese.
Bake for 35–40 minutes, or until the filling is set and golden brown.
Let the leek quiche cool for 5–10 minutes before slicing and serving.