1 Start the dough: In the bowl of a stand mixer fitted with the paddle attachment, combine 3 cups of flour, salt, and 2 tablespoons of sugar.
2 Bloom the yeast: In a 4-cup measuring glass or medium bowl, combine the warm milk (it should be about 100°F), remaining tablespoon of sugar, and yeast, and allow it to sit until foamy, about 5 minutes.
3 Make the dough: Beat the egg into the foamy milk mixture and add the mixture to the mixing bowl of flour. Mix by hand or using the paddle attachment with your stand mixer set to low or medium low, until you get a wet dough with shaggy dry bits throughout. This can take anywhere from 30 seconds to 1 1/2 minutes depending on how you’re mixing.
Swap out the paddle attachment for the dough hook. Add the melted butter. Set the mixer to medium-low until the butter is incorporated, about 1 minute.
4 Knead the dough: Turn the mixer up to medium or medium-high (depending on the size and weight of your mixer) and knead on the hook for about 6 minutes. The dough should be tacky to the touch but not so wet that you can’t handle it.
5 Shape the dough and let it rise: Shape the dough into a ball and place it in a greased bowl. Cover with plastic and allow it to rise until doubled in size, 1-2 hours depending on the temperature of the room.
6 Set up your frying and dusting stations: Fill a large 4-quart pot with a few inches of vegetable oil (about 2 quarts). Set a cooling rack over a baking sheet and place it next to the pot of oil along with tongs.
Sift 3 cups of powdered sugar into a medium-sized mixing bowl and set next to the rack and a sheet pan.
7 Cut the dough and heat the oil: Once the dough has risen, turn it out onto a floured surface and roll it out into an oblong shape (about 10 inches by 14 inches and 1/4 inch thick). Cut the dough into 12 rough rectangles and cover with a flour-dusted tea towel to rest while you heat the oil.
8 Fry the beignets: Heat the frying oil to 325℉. Fry the beignets in batches until golden, about 1 1/2 to 2 minutes per side.
9 Drain and coat the beignets in sugar: Use your tongs or a frying spider to lift the beignets out of the frying oil and place them on the baking rack.
Let some of the fat drain off for about a minute before covering in powdered sugar. You want to coat them with sugar while the beignets are still hot, but not straight out of the fryer dripping in oil. Drop the drained beignets into the bowl with the powdered sugar. Turn to coat. Repeat with the remaining beignets.
10 Serve: Serve warm with another generous dusting of powdered sugar and hot coffee on the side.