Whatever you call it, it's a rich bread dough, it's fried, it's sweet. IT'S A PARTY!
There are many versions and names of these fried doughnuts and they are all correct. Depending on your ancestry or geography or morphing of neighborhood cultures all over the USA or in many other countries (Germany, Switzerland, Poland, Italy, etc.) you can find some form of these served up on Shrove Tuesday or Mardi Gras or Carnival or whatever else it's called: the day before Ash Wednesday. This date changes every year but it's always six weeks before Easter, sometime between February 4th and March 10th. Growing up, my family per se had no regular tradition for this day, although we had plenty for other Catholic feast days or observances. I recall on one occasion, though, that my Grandma Pilewski fried up leftover Sweet Bread dough for us. This was a rare and unbelievable treat: nice warm yeast doughnuts dipped in sugar.
Of course, I can't leave well enough alone. I got to poking around on the internet and was happy to find plenty of references to "Fasnachts" but many of the recipes were from the Pennsylvania Dutch and had potatoes in them. This site by Susie J had a clear recipe and some history behind it. The ingredients were the same as Polish Sweet Bread, just in different proportions. I decided to follow her recipe exactly. I made one batch on the Monday before Shrove Tuesday. They turned out tasty, they looked pretty. I delivered a bag of them to Debbie-My-Egg-Lady for her bread of the week and packed up some for a a few other friends. However: while Susie J's version tasted good, they were different from what I had been used to. As I continued to taste them, I realized that a certain "yeastiness" was lacking. I was having some girlfriends over for Fasnachtkuechle and coffee for Shrove Tuesday so I had time to go back to making the Sweet Bread version for them. I decided it was worth a trip to the bakery to purchase a pound of cake yeast. I really wanted to determine if the yeast was the big deal. As it turned out, yes it was! I played around a bit with the proportions of the ingredients, so I wouldn't follow this recipe for Sweet Bread. (That will be posted for Easter.)
1.5 oz cake yeast dissolved in 1/4 c lukewarm water
2 c milk
1/2 c (1/4 #) butter
2/3 c sugar
9 cups or so AP flour
1 T salt
powdered sugar and granulated sugar for dipping
Scald the milk; remove from heat (microwave is fine). Melt the butter in the hot milk and let cool to lukewarm; stir in the sugar and and eggs and the yeast slurry. Place half the flour and all the salt in the bowl of a stand mixer. Pour the wet mixture into the flour and salt and beat well. Continue adding the flour one cup at a time until you have a sticky dough. Using the dough hook, knead for a few minutes. It will not be as stiff as a regular bread dough. Cover and let rise until double. (This is the equivalent of three packets of yeast, so it should rise in an hour.) Cut the dough into two or three pieces and pat them into rounds. Roll them out on a floured board to about 1/3-1/2 inch thickness. Using a pizza cutter (a knife drags the dough), cut into squares or rectangles about 2" x 3" or as you prefer. Cut them all out before frying; place a towel over them until they are ready to go into the frying pan. You don't have to let them rise a second time before cooking, but it's fine if they do rise. (They will puff up pretty nicely once they hit the hot oil).
Heat about 2" of oil (I used peanut and vegetable oil because that's what I had on hand) in an electric frying pan or dutch oven or even a wok. It helps to use a thermometer to make sure the oil stays as even a temperature as possible- you want to keep it between 350F and 375F. If it's too hot the surface will brown too quickly and the inside will still be doughy. Don't crowd too many in the hot oil at one time. Turn them over after a minute or two and fry for another minute or so. Check one to make sure the inside is cooked. There might be a white "waist" on the doughnuts as they fry- this is normal. Sometimes they are so puffy they won't stay turned over once the first side is cooked. I find it helpful to use a wire skimmer or "spider" to handle them. Cover cookie racks with brown paper or paper towels and place the cooked fasnachts on them to drain. While still warm, dip some into shallow plates of powdered sugar and some into powdered sugar (or to your preference.) Cinnamon sugar is good too! You can also put a few at a time into brown paper bags with the sugar inside- close the bag and shake carefully until coated.