- Scald milk and let cool to 110 degrees. Transfer to a large mixing bowl or stand mixer. Add the butter, sugar and vanilla and, using the dough hook, mix until sugar is dissolved. Add the yeast and mix again until dissolved.
- Scrape down sides of bowl and add eggs, 1 at a time, mixing after each addition. With mixer running on low speed, add flour a few tablespoons at a time. You may not need all the flour, or you may need more. Mix until a smooth dough is achieved. Cover and let rise in same mixing bowl in a warm, draft-free place for 1 hour.
- When dough has risen, lightly coat a baking sheet with cooking spray. Lightly dust your work surface or a silicone mat with flour, and pull out a handful of dough at a time. Roll to 3/4-inch thick. Cut with a 2 1/2- to 3-inch round cutter (no hole in the middle). Transfer cut circles to sprayed pan. Pick up scraps and re-roll.
- When all the dough has been cut, cover and let rise until doubled in bulk, 30 minutes or longer. Usually, by the time all the dough has been cut, the first pączki are ready to be fried.
- Pour about 2 inches of oil into a cast-iron skillet or heavy-bottomed pot and clip on a frying thermometer. Heat oil to 350 degrees. Fry up to 6 pączki at a time for 3 minutes or until golden on the bottom. Flip with a skewer, tongs or a fork (without piercing the pączki), and fry the other side for another 3 minutes or until golden. Watch carefully, because they can burn easily. Keep your eye on the thermometer and adjust the heat as needed to maintain 350 degrees. Using tongs, remove the pączki to a paper-towel-lined sheet pan.
- When cool enough to handle, use a sharp paring knife or small serrated knife to make a 1 1/2-inch slit in the side of pączki, just large enough for a spoon to fit. Fill with a generous teaspoon of filling of choice (Maria uses her homemade strawberry jam). Roll filled pączki in granulated sugar or dust with confectioners' sugar.
- Pączki are delightful warm but Maria says hers will keep for several days. She also freezes them to good effect before rolling in sugar.
Note: Always use caution when working with hot oil, especially around children. Have a fire extinguisher designed for grease fires at the ready.