Grease the slow cooker crock with cooking spray. Spread hash browns to cover the bottom of the prepared crock.

Whisk beaten eggs, milk, mustard, salt, and black pepper together in a large bowl until well combined. Set aside.

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 hash browns, then sprinkle cheese on top. Pour egg mixture over cheese.

Cook on Low for 6 to 8 hours.