Combine the yeast, two tablespoons of granulated sugar, and the warm water in a bowl and mix well with a fork. Let the mixture stand until it is foamy, about 5 to 10 minutes. Next, add the milk, egg, melted butter, salt, and the remaining two tablespoons of granulated sugar and mix with a fork to combine. Add the flour in two or three batches and mix until you have a sticky dough. If you have one, you can use a stand mixer with the dough hook attachment at medium speed.

Lightly grease a large bowl with vegetable oil. Add the dough and coat it in the oil. Cover the bowl with plastic wrap and let it stand at room temperature for 2 to 3 hours. The dough should be very puffy and doubled in size.

Heat three or four inches of oil, about two quarts, over medium heat to 350° in a heavy pot with high sides, such as a Dutch oven.

While the oil is heating, turn out the dough on a lightly floured surface and cut it in half. Working one batch at a time, use a lightly floured rolling pin to roll the dough to about ¼ inch thick. Depending on how big you would like your beignets, cut the dough into 1 to 2-inch squares, set aside on a floured surface, and repeat with the remaining dough.

Place the powdered sugar in a medium-sized bowl.In small batches of 2 to 3 beignets, fry the dough until it puffs and is golden on the bottom side, only 1 to 2 minutes per side. Next, flip the beignets and fry until golden on the second side. Transfer the beignets to a baking sheet with a cooling rack placed over it or on a paper towel-lined baking sheet.

When the beignets are cool enough to touch, roll them in powdered sugar. Before serving, dust with more confectioners’ sugar and serve warm.