Proof the Yeast: In a small bowl, combine the yeast with warm milk and a teaspoon of sugar. Allow it to sit for 10–15 minutes, or until it becomes frothy.

Mix the Wet Ingredients: In a large mixing bowl, whisk together the egg yolks, granulated sugar, and vanilla sugar until pale and creamy.

Combine Ingredients: Add the activated yeast, melted butter, rum (or Spirytus), and a pinch of salt to the egg mixture.

Knead the Dough: Knead the dough on a floured surface for 8–10 minutes, or until it becomes smooth and elastic.

Let the Dough Rise: Place the dough in a lightly greased bowl, cover it with a clean towel, and let it rise in a warm place for 1–1½ hours, or until doubled in size.

Portion and Shape: After the dough has risen, punch it down and divide it into 12–15 equal portions. Roll each portion into a ball and arrange them on a lightly floured surface. Cover with a towel and allow them to rise for 30 minutes.

Preheat the Oil: Warm the canola oil in a deep pot over medium heat until it reaches 350°F (175°C). Test with a small piece of dough—it should sizzle and turn golden in about 1 minute.

Cook the Pączki: Fry the doughnuts in batches, cooking for 2–3 minutes per side, or until they are golden brown. Use a slotted spoon to remove them and let them drain on paper towels.

Fill the Pączki: Use a piping bag fitted with a narrow tip to inject jam into the center of each donut.

Prepare the Glaze: In a bowl, whisk together powdered sugar and lemon juice until smooth. Drizzle or brush the glaze over the warm doughnuts.

Serve Fresh: Enjoy the Pączki warm, or let them cool completely before serving. These donuts are best eaten fresh on the day they’re made.