Prepare Cabbage: Remove tough outer leaves, quarter the cabbage, remove the core, and slice into 1/4-inch thin ribbons.
Grease Slow Cooker: Lightly grease a 5- to 6-quart slow cooker with a small amount of the melted butter.
Layer Cabbage: Spread half of the cabbage ribbons evenly across the bottom.
Layer Noodles: Scatter half of the uncooked egg noodles over the cabbage. Avoid packing them too tightly.
Season: Drizzle half of the melted butter over the noodles and cabbage. Sprinkle with 1 teaspoon of black pepper.
Repeat: Add the remaining cabbage, then the remaining noodles. Drizzle with the rest of the butter and the remaining pepper.
Cook: Cover and cook on HIGH for 2.5 to 3 hours or LOW for 4 to 5 hours. Do not lift the lid during the first 2 hours.
Toss: Once the time is up, gently toss the ingredients together. The cabbage should be tender and caramelized at the edges.
Finish: If noodles aren't fully soft, cook for another 20 minutes. Adjust seasoning with extra pepper if desired.
Serve: Switch to the "Warm" setting and serve directly from the slow cooker.