Preheat oven to 325 degrees F (165 degrees C). Grease an 8x11-inch baking dish.
Cook and stir breakfast sausage in a skillet over medium heat until browned and crumbly, about 10 minutes; drain excess grease. Mix green onion into sausage and spread mixture over bottom of the prepared baking dish. Spread hash brown potatoes in a layer over sausage; top with Cheddar cheese.
Whisk eggs, milk, and gravy mix together in a bowl until smooth; pour over casserole. Season with paprika.
Bake in the preheated oven until a knife inserted into the center of the casserole comes out clean, about 1 hour. Let stand 10 minutes to firm up before serving.
