Gently place the pie crust into a 9-inch pie plate with shallow sides, crimping the edges for a decorative touch. Prebake the crust for 10 to 12 minutes until it's just starting to turn golden.
After the crust has cooled for a few minutes, evenly distribute the chopped ham and the mixed cheeses across the bottom of the crust.
Whisk together the milk, eggs, garlic salt, and pepper in a medium bowl. Carefully pour this mixture over the ham and cheeses in the crust, taking care not to overfill.
Bake the quiche for 45 to 50 minutes. It's done when you can insert a knife into the center and it comes out clean. The quiche should be set and the top lightly browned.
Let the quiche rest for 5 to 10 minutes before slicing. This allows it to set completely, ensuring perfect slices.