01 - In a small bowl, combine warm water, 1 tablespoon of sugar, and yeast. Stir and let sit for 5–10 minutes until foamy.
02 - In a large mixing bowl, whisk together the milk, remaining sugar, egg, butter, and vanilla extract. Add the yeast mixture and mix until combined.
03 - Gradually add the flour and salt, mixing until a sticky dough forms.
04 - Turn the dough onto a floured surface and knead for about 5 minutes until smooth and elastic.
05 - Transfer the dough to a greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm place for about 2 hours, or until doubled in size.
06 - Once risen, punch down the dough and roll it out on a lightly floured surface to about 1/4-inch thickness. Cut the dough into 2 1/2-inch squares.
07 - Heat oil in a deep fryer or heavy pot to 350°F. Fry beignets in batches, turning occasionally, until puffed and golden brown on both sides (about 2–3 minutes per batch).
08 - Remove with a slotted spoon and drain briefly on paper towels. Generously dust warm beignets with powdered sugar and serve immediately.