Preheat the oven to 400°F (200°C). Grease a 9-inch pie plate.
In a bowl, combine the thawed hash browns and melted butter. Press the mixture evenly into the bottom and sides of the pie plate to form a crust.
Bake the crust for 20–25 minutes, or until lightly golden.
Sprinkle the diced ham, shredded cheddar cheese, and green onions evenly over the crust.
In another bowl, whisk together the eggs, milk, salt, and black pepper.
Pour the egg mixture over the filling.
Reduce the oven temperature to 350°F (175°C) and bake for 25–30 minutes, or until the center is set and the top is lightly browned.
Let the pie rest for 5–10 minutes before slicing and serving.