Pączki (Jam-Filled Doughnuts)

Switch to a dough hook, add the yeast mixture and the flour, and mix on the lowest speed until combined, 2 to 3 minutes. Increase to low and mix, gradually adding the butter to incorporate into the dough. It will seem very loose and glossy but at about the 3-minute mark the dough will start to come together more. (This is a very sticky dough, but does not require more flour.) Continue mixing on low for 15 minutes, scraping down the sides occasionally, until the dough starts to mostly pull away from the sides of the bowl (it won’t clean the sides).

Lightly brush a large bowl with oil and transfer the dough to the bowl using a dough scraper. You can also lightly wet your hands before transferring the dough. Cover the bowl with a kitchen cloth and place in a warm spot to rise until doubled in size, about 1 1/2 hours. (If your kitchen is on the cooler side, place the dough in a turned-off oven with the oven light on.)

When the dough has doubled in size, gently deflate the dough by gently pressing down (it will still be tacky), cover again and return to a warm spot to rise again until doubled in size once more, about 30 minutes.

Line a baking sheet with parchment paper. Very lightly flour a work surface. Gently deflate the dough, transfer to the work surface with the help of the dough scraper, and knead a few times. (The dough will still be tacky.) Using a rolling pin, evenly roll out the dough to a 2/3-inch thickness. Use a 3-inch round cutter to cut out rounds of dough, placing the cuts close to each other so you use up as much dough as possible. Place each round of dough on the prepared sheet, leaving about 1 inch in between dough rounds, and cover with a kitchen cloth. (You may need two baking sheets.) Gather up the remaining dough scraps into a ball and let rest for a few minutes. Roll out and cut out as many pieces as you can to end up with about 16 pączki. (Avoid re-rolling out the dough more than once.)

Place the covered baking sheet back in a warm spot and allow dough rounds to rise for 30 to 45 minutes, until puffy.

Halfway through the rising process, set up your frying station: Fill a 5-quart deep pot or Dutch oven with 1 inch of oil and attach a deep-fry thermometer. Heat the oil over medium until it reaches 350 degrees. Place a wire rack on a sheet pan (you can line the sheet pan with parchment for easier cleanup), or line a sheet pan with paper towels.

Start by frying a batch of “test” doughnuts: Make sure the oil is at 350 degrees. Carefully place three pączki top side down in the oil and fry until a deep brown on the bottom, 2 ½ to 3 minutes. (Pączki should be a deeper brown than regular donuts.) Using a slotted spoon or chopsticks, flip the pączki and fry the other side until brown, 2 ½ to 3 minutes more. (The temperature will drop when the pączki are added to the pot, but will start climbing more rapidly as the pączki fry. Watch the oil temperature carefully and adjust the heat gradually as needed to maintain 340 to 350 degrees.)

Check the doneness: Remove the pączki with a slotted spoon and place on the prepared sheet pan; turn off the heat under the pot while checking doneness. If you have a thermometer, take the internal temperature of one of the pączki, which should be about 190 degrees. Or when cool enough to handle, cut into it and make sure the inside has cooked and the dough isn’t raw. Adjust cooking time as needed.

Return the pot to medium heat until the oil reaches 350 degrees. Fry the remaining pączki, three at a time, keeping a close eye on the temperature and adjusting as needed. As each batch of pączki is removed from the oil, immediately replace with three more rounds of dough. This will help keep the oil temperature stable. (Unfilled fried pączki can be stored at this point at room temperature for up to 1 day.)

To fill: Fill a piping bag with jam. When cool enough to handle, make a small hole in the side of a pączek using a chopstick or skewer, then insert the tip of the piping bag and squeeze until the filling starts to spill out. (You’ll use about 1 tablespoon per doughnut.)

To finish: While they are still warm, dust the filled pączki with powdered sugar; roll in a wide bowl of granulated sugar; or brush with pączki glaze and top, if desired, with candied orange peel. Pączki are best shared and eaten right away. (If necessary, filled pączki can be stored in an airtight container in the fridge for 1 to 2 days.)