Combine cabbage, 1 teaspoon salt, and water to cover in a medium Dutch oven. Bring to a boil. Reduce heat; cover and simmer 25 minutes. Add sausages; cover and simmer an additional 30 minutes. Remove sausages; set aside, and keep warm. Drain cabbage and chop; set aside.
Combine potatoes, butter, remaining salt, and pepper in a large mixing bowl; beat until well blended. Add chopped cabbage, and stir until well blended. Spoon cabbage mixture onto a warm serving platter. Place sausage links on top of cabbage mixture, and serve immediately.