In a medium-size bowl, mix hash browns, Parmesan cheese, salt, and pepper together; set aside.
In a small bowl, mix eggs and milk together; set aside.
Coat the interior of the crockery insert 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 onion, bacon, and Swiss cheese evenly across the bottom of the potato “crust.” Pour the egg and milk mixture into the crust, then cook on low 3-½ to 4 hours. If your slow cooker has a warming setting, you can keep the flan warm several hours; if it doesn’t, the flan will stay servable up to 1 hour with the cooker turned off. Cut into squares or wedges to serve.