Preheat oven to 425 degrees F (220 degrees C). Squeeze and drain any excess moisture from hash brown potatoes.
Stir potatoes and butter in a bowl; press mixture into the bottom and up the sides of a 10-inch pie dish to make a crust.
Bake crust in preheated oven until lightly browned, 25 minutes.
Beat heavy cream and eggs in a bowl. Remove potato crust from pie dish and break apart; stir potatoes into egg mixture in a bowl. Layer ham and Monterey Jack cheese blend into bottom of the empty pie dish; pour egg-potato mixture over ham and cheese.
Bake quiche in preheated oven until eggs are set, about 30 minutes.