Activate The Yeast: Whisk warm water, yeast, and sugar in a bowl. Let it sit for 5 to 10 minutes until the yeast dissolves and starts to foam. If it doesn't bubble, the yeast is dead and won't work.
Add The Egg: After activating the yeast, add the egg and milk to the bowl. Whisk until well combined. Room temperature egg and milk work best.
Make The Dough: Stir flour and salt in a stand mixer. Add the yeast mixture and butter. Mix on low speed for about 5 minutes with the dough hook until the dough comes clean from the sides of the bowl.
Let It Rise: Transfer the dough to a greased bowl, cover, and let it rise in a warm, dark place for 1 to 2 hours until it doubles in size.
Form The Beignets: Roll out the dough into a ¾-inch thick rectangle. Cut into strips, then squares.
Heat The Oil: Heat 2 to 3 inches of vegetable oil to 350°F (177°C) in a deep frying pan. Use a thermometer to monitor the temperature.
Fry The Beignets: Fry 5 to 6 squares at a time for 2 to 3 minutes, turning once, until golden brown. Transfer to a paper towel-lined sheet.
Dust And Serve: Sprinkle powdered sugar on the beignets and serve immediately. Optional: add cinnamon or vanilla sugar for extra flavor. Enjoy!