Preheat your oven to 375°F.
Gently unroll the pie crust and fit it into a 9-inch pie plate. Crimp the edges for a decorative touch.
In a large mixing bowl, whisk together the eggs, milk (or cream), salt, and black pepper until well combined.
Evenly distribute the chopped ham, 1 cup of shredded cheese, and green onions over the crust. Carefully pour the egg mixture on top. Finish by sprinkling the remaining 1/2 cup of cheese over the egg mixture.