Preheat oven to 375°F. Place pie crust in a 9" pie plate. Crimp or decorate edges if desired.
Whisk eggs, milk or cream, salt, and pepper in a medium bowl until smooth.
Layer ham, 1 cup of cheese, and green onions evenly into the crust.
Pour the egg mixture over the filling. Top with remaining ½ cup of cheese.
Bake uncovered for 35–40 minutes, or until the center is fully set.
Cool slightly (5–10 minutes), then slice and serve warm.