Preheat your oven to 375°F (190°C).
Roll out the pie crust into a 9-inch pie plate and crimp the edges.
Sprinkle the grated Gruyère cheese and diced ham evenly over the bottom of the pie crust.
In a mixing bowl, whisk together the eggs, milk, heavy cream, salt, and pepper.
Pour the egg mixture over the cheese and ham in the crust.
Bake the quiche in the preheated oven for 40-45 minutes, or until the filling is set and the top is golden brown.
Allow the quiche to cool for a few minutes before slicing and serving.