In a bowl, combine hash browns, Parmesan, cayenne, salt, and pepper; set aside.
In another bowl, mix eggs and milk together; set aside.
Coat the interior of a 4- to 6-quart oval slow cooker with cooking spray and pack half of the hash brown mixture in an even layer, completely covering the bottom of the insert. Press the remaining hash brown mixture up the sides to a height of about 2 inches. Scatter onions, bacon, and Swiss cheese evenly across the bottom of the potato “crust.” Pour egg mixture into the crust, then cover and cook on low for 3-½ to 4 hours. Cut into squares or wedges to serve.