Preheat the oven to 400 degrees F (200 degrees C).

Remove and wash outer leaves from cabbage; line a 9x13-inch baking dish with the leaves to cover the bottom entirely. Shred remaining cabbage.

Combine shredded cabbage, potatoes, and sausage in a large bowl; spread over cabbage leaves in the baking dish.

Whisk together milk, beaten eggs, salt, and pepper in a large bowl until well combined; fold in bread cubes. Set aside until bread absorbs some liquid, 1 to 2 minutes; pour over cabbage mixture. Dot with butter.

Bake in the preheated oven until potatoes are tender and the top is lightly browned, about 45 minutes.