Spray the insert of a slow cooker with cooking spray (for easier clean up) and preheat on high.
In a medium saucepan, add the milk, 1 cup half-and-half, 1 tablespoon butter, and polenta. Season with salt and bring to a boil over medium-high heat, whisking constantly to keep the mixture lump-free. Boil for 2 to 3 minutes. Pour the mixture into the slow cooker and cook on high for 2 hours, stirring once or twice per hour. Once you are ready to serve, open the slow cooker and whisk in the remaining 1 tablespoon butter, remaining 1/3 cup half-and-half, and Parmesan.