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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.
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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.
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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.
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Now punch it down, then wrap it back up and allow it to rise again for 1 to 2 and 1/2 hours.
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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.
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Heat your oil to 350 degrees F.
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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.
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Scoop out of the fryer and lay on a paper towel, then dunk in desired topping. Place on a rack to dry.
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Repeat with 3 or 4 at a time so you don't over-crowd your oil. Continue until all the pacski are cooked.
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Serve with a big old sugary smile!