Cover potatoes with cold salted water by 1 inch and bring to a boil, then boil, uncovered, until tender when pierced with a sharp knife, about 18 minutes. Drain in a colander.
Heat butter in a 10-inch heavy nonstick skillet over moderately high heat until foam subsides, then sauté cabbage with salt and pepper, stirring frequently, until tender, about 5 minutes.
Add potatoes, mashing and stirring them into cabbage while leaving some lumps and pressing to form a cake. Cook, without stirring, until underside is crusty and golden, about 10 minutes. Serve immediately.