Use a 3-inch biscuit cutter to cut out rounds of dough. Transfer the dough rounds to parchment-lined baking sheets. Gather scraps of dough and again roll out and cut until you have used up all of the dough. Cover the baking sheets loosely with plastic wrap and place in a warm, draft-free spot until almost doubled in size, about 30 minutes.
Meanwhile, heat at least 1½ inches of oil in a heavy-bottomed pot or deep skillet (I used a 12-inch cast iron skillet) over medium heat to 350 degrees F. Carefully lower about six paczki into the oil at a time (be sure not to overcrowd the pan) and fry until the bottom is golden brown. Carefully turn them over and continue to fry until the other side is golden brown. Use a spider strainer or slotted spoon to remove them to a paper towel-lined baking sheet to drain. Allow the oil to come back to temperature, then repeat until all of the paczki have been fried.
Allow the paczki to cool until you are able to handle them easily. Using a filling tip, pipe fruit preserves into the sides of the paczki, then roll in sugar. The paczki is best the same day they are made but can be stored in an airtight container at room temperature for up to 2 days.
