Paczki: in a large bowl or the bowl of your stand mixer, weigh out and add all-purpose flour, sugar, salt, yeast, egg yolks, brandy (or rum), milk, melted butter, and vanilla extract.

If you are kneading by hand, stir the mixture with a spoon until it all comes together, and then knead for 15 minutes until you have a smooth dough. If you are using a stand mixer, knead for 8 minutes on medium speed using the dough hook.

Move the dough into a lightly oiled bowl and leave it in a warm spot in your kitchen for 1.5 to 2 hours to rise. After this initial rise, I like to put the dough in the fridge overnight. This isn't required, but it helps with the shaping process. 

After the dough has risen, gently deflate it and move it to a lightly greased or floured surface. Using a rolling pin or your hands, form the dough into a rough rectangle and roll out or flatten it to about 1/4 to 1/2 of an inch in height. 

Using a round cookie or biscuit cutter (or even a sharp-edged glass or cup) cut out 2.5-to-3-inch circles. Place each circle onto a sheet pan lined with parchment and cover with plastic wrap or a second inverted sheet pan and allow the dough to rise again for 30 minutes. Do not discard any extra dough after cutting it into circles. Push leftover dough together and re-roll and re-cut until you have used all the dough. 1/4 inch thick seems thin, but these puff up big in the frying process. 

In a wide pan or dutch oven, bring 1.5 to 2 inches of peanut or vegetable oil up to 350 degrees F (175 C). 

Fry 2 or 3 paczek at a time, for about a minute per side until golden brown. Flip and fry on the second side for another minute. 

Remove each paczek to a cooling rack set inside a sheet pan to cool. If you want the top covered in powdered sugar, you should sprinkle that on when the paczek is hot. 

Italian beef and au jus: season your beef liberally with salt and pepper. 

In a large Dutch oven or oven-safe pot, brown all sides of the beef over medium-high heat. Once the meat is browned, move to a to plate to rest while you get everything else ready. Do not clean out the pan. 

Preheat the oven to 325 degrees F (162 C). 

Add beef base and 4 cups of beef broth together in the pot that you used to brown the beef. Add all the spices and herbs. 

Add beef back to the Dutch oven. Make sure the liquid is at least half of the way up the side of the beef. If it is not, add up to one cup of water. 

Roast beef for 2 to 2.5 hours adding more broth or water as needed to keep the liquid at least halfway up the beef. Add more stock or water if needed. 

Remove the pot from the oven and allow the beef to cool off on a cutting board for at least half an hour. Once the meat is cooled a little, wrap it up or add it to a large container and place it in the refrigerator to cool fully. Cool beef for at least 4 hours or overnight. 

Strain the broth into a container and store it in the refrigerator as well. 

When the beef has fully cooled in the refrigerator, remove it and place it on a cutting board. Using a very sharp serrated knife, slice the beef as thinly as possible. Be very careful and patient and shave the meat as thin as you can. 

Giardiniera custard: chop 1/2 cup of giardiniera until it's in pieces smaller than 1/4-inch square. Place the chopped giardiniera in a bowl for later.

In a large bowl, whisk together eggs, sugar, and cornstarch until the sugar is fully dissolved. 

Place a pot over medium heat add milk, vanilla extract, and butter, and cook until the liquid just starts to simmer. Do not allow it to start boiling. Once the milk is simmering, reduce the heat to low and slowly add the egg mixture, whisking the pot constantly.

Once both the milk and the egg mixtures are combined, cook, while still whisking for 5 to 10 minutes until the custard starts to thicken. After it has thickened, add the chopped giardiniera and whisk until the vegetables are fully combined into the custard. Move the custard to a sealed container and place in the refrigerator for up to 3 days. 

Sandwich assembly: In a small pot, bring 1/4 to 1/2 cup of au jus up to a simmer. 

Add a big handful of sliced beef to the au jus/gravy in the pot. Warm beef in the pot for 3 to 5 minutes until everything is warm. 

Slice a paczki in half and spread some giardiniera custard on the bottom half. Top the custard with some warmed beef, straight from the pot. Add extra giardiniera to the top of the beef if desired. Place the top of the paczki on top of the sandwich and dust the top with powdered sugar (if desired).

Serve the sandwich with a little hot au jus for dipping.