Heat olive oil on medium in large skillet. Add onion and cook for 3 minutes. Add mushrooms, cook until onion is translucent & liquid from mushroom has evaporated about 5 minutes. Add ham and stir.
Add mixture to pie shell. Sprinkle 2 cups of cheese on ham mixture.
Beat eggs, milk, and pepper together and pour over quiche. Add remaining cheese on top.
Bake on a parchment lined baking sheet for 30-35 minutes, or until cooked through.