Spray the crock of your slow cooker with cooking spray. Spread hash brown potatoes into the bottom of the crock.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Spread sausage over the hash brown potatoes; top with Cheddar cheese.
Beat eggs and milk together in a large bowl; add ground mustard and generously season with salt and pepper. Mix seasonings thoroughly into the egg mixture; pour over the cheese layer in the slow cooker.