Step 1

Soften the butter. Cut 7 tablespoons unsalted butter into 14 pieces and let sit on the counter at room temperature until softened.

Step 2

Mix the eggs and flavorings. Place 5 large egg yolks, 2/3 cup granulated sugar, 1 1/2 teaspoons kosher salt, 1 tablespoon vanilla extract, and 2 tablespoons water or alcohol of choice in a medium bowl. Whisk until pale and fluffy and the sugar is dissolved, about 3 to 4 minutes.

Step 3

Add warm milk. Heat 1 1/3 cups plus 1 tablespoon milk in the microwave (about 30 seconds) or on the stovetop until lukewarm. Add to the egg mixture and whisk to combine.

Step 4

Mix the dry ingredients. Place 5 1/3 cups all-purpose flour (700 grams) into the bowl of a stand mixer. Add 2 tablespoons instant yeast if doing a same-day rise, or 4 teaspoons if doing an overnight rise, and whisk to combine.

Step 5

Mix the wet and dry ingredients together. Pour the egg mixture into the flour. Attach the dough hook and turn the mixer on to the lowest speed and mix until all the ingredients are well incorporated, the dough clears the sides of the bowl, and is smooth, tacky, and stiff when poked, about 6 minutes. Don’t be tempted to add any additional liquid, the mixer will be working hard!

Step 6

Mix in the oil. Mix in 2 tablespoons vegetable oil, one tablespoon at a time, about 3 minutes.

Step 7

Mix in the butter. Keeping the mixer on the lowest speed, add the softened butter one to two pieces at a time, letting each piece fully mix in before adding the next, about 13 minutes total. Stop the mixer occasionally to push the dough off the hook. When ready, the dough should form a fairly smooth, firm, and not sticky ball, and the sides of the bowl should be clean.

Step 8

Let the dough rise in the refrigerator. Remove the dough from the bowl, lightly coat the bowl with vegetable oil, and place the dough back in. Cover the bowl with plastic wrap and refrigerate until at least doubled in size, 2 1/2 to 3 hours (or overnight if using 4 teaspoons yeast). Meanwhile, prepare the parchment paper squares.

Step 9

Cut parchment paper squares. Cut 21 (4-inch) parchment paper squares.

Step 10

Divide the dough. Transfer the dough to a work surface (don’t knead or fold it anymore) and divide into 21 pieces (each about 65 grams).

Step 11

Form the dough balls. Working with one dough ball at a time, fold the sides in towards the center and pinch together. Place seam-side down on the work surface. Using the palm of your hand, roll and press it lightly against the surface to form a smooth, tight ball. Let rest uncovered for 10 to 15 minutes.

Step 12

Flatten and let rise again. Place a ball on a parchment square. Flatten with your palm into a 1/2-inch thick disc that’s about 3-inches wide. Repeat with the remaining dough balls. Cover loosely with plastic wrap and let rise until at least doubled in size, about 1 1/2 hours.

Step 13

Heat the oil. About 15 minutes before the end of the rising time, heat 1 1/2 quarts vegetable oil in a large Dutch oven or heavy-bottomed pot until 340ºF. Line a large baking sheet with paper towels or fit a wire rack over the baking sheet.

Step 14

Fry the pączki. Working in batches of 5 to 6 pączki (they will puff and expand a lot), gently place each one upside-down in the hot oil and peel off the parchment. Fry until dark golden brown and the center registers 193ºF, about 3 1/2 minutes per side. Transfer to the prepared baking sheet. Repeat frying the remaining pączki, taking care to maintain an oil temperature of 340ºF.

Step 15

Filling option 1: With a piping bag. While still warm, take a chopstick or paring knife and poke it through the side about halfway into the pączki. Wriggle the chopstick or knife inside a bit to hollow out space for the filling. Fit a 1/4-inch round tip onto a piping bag, then fill the bag with 1 1/2 cups jelly. Pipe about 1 tablespoon jelly into each pączki through the hole in the side.

Step 16

Filling option 2: Like a sandwich. While still warm, halve each pączki horizontally with a serrated knife. Open them up, place 1 tablespoon jam or jelly on the bottom half of each one, then close with the top half.

Step 17

Top the pączki (optional). If desired, dust with powdered sugar before serving. Another option is to glaze the filled pączki (let them completely cool first): whisk 3 cups powdered sugar with 1/3 cup hot water in a medium bowl until smooth, then dip the top of each pączki into the glaze. Top with chopped candied orange peel if desired and let the glaze set, about 15 minutes.