Set a 12-inch nonstick or well-seasoned cast-iron skillet over medium-high heat.

Add 1 tablespoon of the oil to the hot skillet.

Brown the sausage: Put the sliced smoked sausage into the skillet in a single layer.

Cook the sausage for 5 to 6 minutes, turning the pieces now and then, until the edges are browned and the slices look glossy with rendered fat.

Transfer the sausage from the skillet to a plate and leave any fat in the skillet.

Cook the cabbage: Add another 1 tablespoon of oil to the skillet, then add the sliced onion, sliced cabbage, caraway seeds, and 1/2 teaspoon of the salt.

Cook the cabbage mixture over medium heat for 3 minutes, stirring often, until the cabbage starts to wilt.

Keep cooking for 8 to 10 minutes, stirring every minute or two, until the cabbage is tender and browned in spots. If the skillet looks dry before the cabbage softens, add 1 to 2 tablespoons of water.

Transfer the cabbage mixture to a bowl and cover it loosely to keep it warm.

Mix the potato cake: While the cabbage cooks, grate the potatoes on the large holes of a box grater into a clean kitchen towel or a colander.

Squeeze the grated potatoes very well over the sink to remove as much water as you can. This helps the potato cake turn crisp instead of steaming.

Put the grated potatoes and grated onion into a large bowl.