Use a whisk and mix flour and salt in a medium bowl before setting aside. Using a microwave, heat the milk slightly, to between 110-115 degrees F. Add the yeast and a tablespoon of granulated sugar. Stir, and leave the mixture for 8-10 minutes to activate the yeast.
In the bowl of a stand mixer, cream the butter and the rest of the granulated sugar together, on medium-high speed, until they’re light and fluffy. Add the whole eggs and blend well before adding the egg yolks and vanilla. Mix again for one minute.
Add the flour mixture, alternating with the yeast mixture. Once the dough has formed, use the kneading hook to combine until the dough is slack and sticking to the sides of the bowl slightly, but not too sticky to work with.
Next, knead dough by hand on flour-dusted surface, forming a smooth ball by tucking the dough under itself. Transfer the dough to a large bowl, cover it with a towel, and leave it to rise and double in size.
Roll out the dough to ½ inch thickness on a floured surface, then cut into 3-inch circles and place on a cookie sheet. Let the dough circles rise and double in size.
Heat oil to 350 degrees F. Dust off any excess flour on their surface, and fry the pączki in batches of 3 to 4 until they’re golden brown on each side. Once done, transfer them to a paper towel-lined baking sheet and let it rest till cool enough to handle.
Place the filling in a pastry bag with a small round tip, and then poke a hole in the middle of each donut using a thick skewer or chopstick. Take care not to poke all the way through. Use the pastry bag to fill the pączki, then glaze them by whisking together the confectioner’s sugar and milk (or simply dust them with powdered sugar). Aim for the consistency of maple syrup when creating the glaze.
Dip the doughnuts into the glaze before letting them rest. Then eat and enjoy!
