Preheat oven to 350 degrees Fahrenheit. Thaw pie crust for at least 15 minutes. Using a fork, prick holes in the bottom and sides of crust to prevent bubbles from forming. Parbake for 12 to 15 minutes, until firm but not browned.

Meanwhile, melt butter in heavy medium skillet over medium heat. Add squash and leek and sauté until tender, about five minutes. Set aside to cool.

Whisk eggs, cream, salt, pepper and parsley in a bowl. Arrange sautéed veggies over bottom of crust, sprinkle with mozzarella cheese and pour egg mixture over it, filling crust completely.

Bake quiche in preheated oven for 30 to 35 minutes, until filling is golden and set in center. Allow to cool slightly before serving.