Mix the half and half, butter, salt, and pepper in a small saucepan and place over a medium-low heat. Cook until the butter melts, but be careful not to let the cream boil.
Put the thawed shredded hash browns into a 13 x 9-inch glass baking dish.
Pour the hot cream and butter mixture over potatoes and sprinkle with the Parmesan cheese.
Bake for around 45 to 55 minutes until the potatoes begin to brown on top. Serve warm.