Make the dough

1. Melt the butter in a small pan over low heat.  Add in the milk.  Heat the milk for a few more seconds until it is just barely warm to the touch.
2. Dissolve in the yeast and a pinch of sugar once the butter.  Let the yeast sit for a couple minutes until you see some foamy bubbles.
3. Add in the rum, lemon zest, vanilla paste, egg yolks and whisk.
4. Pour the yeast/milk mixture into mixer bowl.  Add in the flour and salt. Knead the dough until smooth either by hand or with a dough hook for about 5 minutes in a stand mixer.

First rise

1. Place the dough in a greased bowl. Cover the smooth dough and let rise for 90 minutes to 2 hours.  It will be ready when it’s light and puffy and visibly doubled. 

Roll and cut the paczki

1. Lightly sprinkle a work surface with a little flour. Overturn the bowl with the dough close to the surface, letting the dough fall out without deflating it entirely. Roll the dough into a sheet about 1/3″ thick.
2. Cut out rounds of dough with a 3″ biscuit cutter. Gently press the scraps together. Let the scraps sit before cutting more rounds of dough. Any scraps beyond that can be twisted and fried into unusual shapes.

Second rise

1. Place the dough rounds on a parchment

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   lined sheet pan. Cover with plastic wrap. Allow to sit for a full 30 minutes. This is a critical step because if they sit for less time, they will not have enough air in them to inflate while they fry.

Fry the paczki

1. Clip the candy thermometer

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   to the back side of the pot, making sure that the bottom does not touch the bottom of the pot. Melt the lard and bring it up to 370 F (188 C).
2. Gently place no more than 3 paczki in the pot at a time. Fry for 4 minutes, turning them over halfway through cooking.

Finish the paczki

1. Fish out the finished paczki from the fat with your mesh spider

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   and place on paper towels to drain. Let them cool briefly, and then make a small hole in the side of each donut with the tip of a knife. Fill a pastry bag fitted with a plain tip and fill with your chosen filling.
2. Dust the tops of your paczki with a generous amount of powdered sugar or roll them in a bowl of granulated sugar.
3. Paczki are best eaten fresh from the oil, but custard filled paczki will keep in the fridge for up to 3 days. Jam filled paczki can be kept at room temperature for up to 3 days. In both cases, keep paczki in an airtight container.  You can warm leftover jam-filled paczki in a toaster oven at 350 F for about 5 minutes.