In a stand mixer combine the 1/2 cup sugar and 1/2 cup butter, cream that with a paddle attachment.You want it fluffy before adding anything else. Once it is you can add the egg, egg yolks, rum extract and vanilla extract. Mix until combined.
Now alternately add the flour and yeast mixture to stand mixer bowl. I alternated 3 times and mixed slowly in while adding. Then turn the speed up to a medium speed for a minute or two, until the dough becomes blistered. Every time we make these we end up using the full 5 cups of flour. But I also start out with 4 and 1/2 cups to be sure if I need more or not.
The dough is going to be very sticky, it's okay, don't let that freak you out. Spray a glass bowl with non-stick spray and then set the dough inside. I spray a piece of parchment with non-stick spray then lay that over the top of the dough, then I tightly cover the bowl with tinfoil, sealing the edges. Set the bowl somewhere warm and allow to rise for about 1 to 2 and 1/2 hours, it should double in size.
Now punch it down, then wrap it back up and allow it to rise again for 1 to 2 and 1/2 hours.
Now lightly flour your work surface. Turn your dough out onto the work surface. Roll out so the dough is 1/2 inch thickness. Use a biscuit cutter or glass to cut rounds. Place them on lightly floured pans, cover with a lint free cloth, and allow them to rise for another 30 to 60 minutes.
Heat your oil to 350 degrees F.
Drop pacski in the oil, flat side down, cook for about 2 to 3 minutes, then flip over and cook other side for 1 to 2 minutes. You want them to be golden brown.
Scoop out of the fryer and lay on a paper towel, then dunk in desired topping. Place on a rack to dry.
Repeat with 3 or 4 at a time so you don't over-crowd your oil. Continue until all the pacski are cooked.
Serve with a big old sugary smile!