In a small saucepan, heat milk to between 110-115 degrees F. Pour the milk into a large bowl and add the yeast, stirring to help it dissolve. Add 1 tablespoon sugar and 2 cups of flour to the bowl, mixing until combined and resembling a wet pancake batter.
Cover the bowl with plastic wrap and allow it to rest for 30 minutes in a warm place (or in an oven with a proofing feature) until the mixture has risen and is very bubbly.
In a large bowl or stand mixer fitted with a paddle attachment, cream together butter and remaining sugar until fluffy, 3-4 minutes. Add egg and egg yolks, vodka (or vanilla), and salt, beating until well combined.
Still using the paddle attachment, add remaining flour in 3-4 batches, alternating with the milk-yeast mixture. When a shaggy dough begins to form, fit mixer with a dough hook. Mix for about 5 or more minutes (or knead for 8 minutes by hand) until a soft, smooth, sticky dough comes together. Add another ¼-½ cup of flour if the dough is too soft.
Coat the inside of a large bowl with cooking spray and transfer dough to bowl. Cover with plastic wrap and set in a warm place to rise for 1 hour, until doubled in size.
Turn dough onto a generously floured surface. Dust the surface of the dough with flour, then punch it down until it is about ½-inch high. Use a 2- or 3-inch biscuit cutter (or drinking glass) to cut out rounds. Carefully transfer the rounds to parchment lined baking sheets. Re-roll excess dough and cut as many as possible.
Cover the baking sheets loosely with plastic wrap and set in a warm place to rise for 25-30 minutes, until again doubled in size.
Meanwhile, heat 2 inches of oil in a Dutch oven to 350-360 degrees F, keeping an eye on it while frying (if the oil gets too hot, the outside will burn before the inside is cooked).
Carefully drop the dough rounds in, top side down, a few at a time. Fry 2-3 minutes until golden brown on one side, then flip them and cook another 1-2 minutes until golden. Using tongs, remove them from oil and place on a paper towel-lined baking sheet to drain and dry. Test one to make sure it is completely cooked, and adjust your temperature and cook time accordingly.
If coating in granulated sugar or glazing, do so while the paczki are still warm. For powdered sugar coating, roll them when they are cooled, or dust after filling. Place a straight piping tip in a pastry bag, then fill with raspberry jam (or your preferred filling). Cut ½-inch hole into the side of each paczki with a knife, then pipe 1-2 tablespoons of filling, avoiding overflow.