Preheat oven to 375°F (190°C).
Press hash browns between paper towels to remove excess moisture.
In a bowl, mix hash browns and melted butter. Press into the bottom and sides of a 9-inch pie plate to form a crust.
Bake crust in preheated oven for 20 minutes.
In a bowl, combine ham, cheese, and green onions. Spread over baked crust.
In another bowl, whisk together milk, eggs, salt, and pepper. Pour over ham mixture.
Bake in oven until a knife inserted near the center comes out clean, about 25 minutes.
Let stand for 10 minutes before cutting.