Place crust in a 9 inch pie plate. Bake curst at 400 for about 8 minutes. Whisk the eggs, milk, half and half, salt and pepper together in a medium bowl until frothy and combined; set aside
Sprinkle 1/2 the cheese over the baked pie crust. Top with the ham, then sprinkle with the remaining cheese. Pour the egg mixture into the crust
Bake until the edges are set but the center still jiggles just a little, 30 to 40 minutes. Cool for at least 20 minutes. Serve warm, at room temperature or cold.