For the pastry cream:
2 cups whole milk
1/4 cup white sugar
2 egg yolks
1 whole egg
1/4 cup cornstarch
1/3 cup white sugar
2 Tablespoons butter, cubed
1 teaspoon vanilla extract

In the bowl of a stand mixer fitted with the paddle, stir yeast in the warm milk. Add 2 cups of the flour. Mix and let stand about 1/2 hour, until very bubbly.

Beat the egg yolks and whole egg until light yellow (butter colored) and fluffy.

To the proofed yeast, add the melted butter, sugar, salt, vanilla, and vodka. Add beaten eggs and mix until well blended. Switch to the dough hook and slowly add the rest of the flour to the bowl and knead on low speed until a very soft dough forms. You may not use all of the flour.

Cover the bowl and let rise in a warm place until doubled, about 2 hours.

Meanwhile, make the pastry cream – In a heavy saucepan, stir together the milk and 1/4 cup of sugar. Bring to a boil over medium heat.

In a medium bowl, whisk together the egg yolks and whole egg. Separately mix the remaining sugar and cornstarch; then whisk them into the eggs until smooth. When the milk comes to a boil, drizzle it into the egg bowl in a thin stream while stirring to temper the eggs. Return the mixture to the saucepan, and slowly bring back to a boil, immediately stirring so the eggs do not curdle or scorch on the bottom.

When the mixture comes to a boil and thickens, remove from the heat. The mixture will continue to thicken as you stir. Stir in the butter and vanilla, mixing until the butter is completely melted. Pour into a heat-proof container and cover with plastic wrap directly on the surface to prevent a skin from forming. Refrigerate until completely chilled before using. You could also skip this step altogether and use your favorite fruit preserves.

When the dough has doubled, uncover and punch down. Pat dough onto a floured work surface, down to 1/2 inch.

Using a cookie cutter, glass, or doughnut cutter, gently cut circles and place on silicone or parchment paper lined baking sheets. Cover and let rise for 20 minutes.

Heat oil in a dutch oven to 350F. Working with 3 to 4 at a time, drop doughnuts into the oil and fry on one side until golden brown. Turn over and fry the other side until golden brown. Using a slotted spoon, remove the fried doughnuts and drain on paper towels. Let cool completely.

To fill doughnuts, place the pastry cream or fruit preserves in a piping bag with the tip cut off. Cut the paczki in half and pipe filling onto the bottom half of each doughnut. Top with the other half, and sprinkle with powdered sugar. You can also cut a slit in the side of the doughnut and use a round pastry tip to inject the filling inside, then top with powdered sugar.