Fill a large pot with lightly salted water and bring to a boil.
In a medium bowl, stir together the shredded potatoes, mashed potatoes, egg and onion until well blended. Season with salt and pepper to taste. Combine the flour and baking powder; stir into the potato mixture. The mixture should be thick enough to form into balls.
Process the cottage cheese in a food processor or blender, or run through a sieve. Stir in the egg and salt. Flatten the balls of dough and place a teaspoon of filling into the center. Pinch the dough around the filling to seal it in.
Drop the halushky into rapidly boiling salted water, stir gently once, and cook from 5 to 8 minutes. Remove them to a colander and drain. Place in a serving dish, sprinkle generously with browned butter, and toss lightly. Serve with sour cream.
