1. Melt 1 tablespoon of butter in a heavy 10- to 12-inch enameled or stainless-steel skillet and add the sauerkraut. Fry over low heat, stirring occasionally with a fork, for 3 to 5 minutes, or until the sauerkraut is almost completely dry and has begun to stick lightly to the pan.
2. Then scrape it into a bowl. Melt 3 tablespoons of butter in the skillet and add the onions. Stirring occasionally, fry over moderate heat for 5 to 8 minutes, or until the onions are soft but not brown.
3. Return the sauerkraut to the pan, stir in the sugar, salt and a few grindings of pepper and cover tightly. Cook over low heat for 10 to 15 minutes, then, off the heat, stir in the 2 tablespoons of sour cream. Taste for seasoning.
4. Following the instructions in the varenyky recipe, roll out the dough and cut it into 3½-to 4-inch circles. Fill each circle with 1 tablespoon of the sauerkraut mixture and fold up and cook as directed.
5. To serve, arrange the dumplings side by side on a heated platter and pour the melted butter over them. Serve with a bowl of sour cream.
