01 - Combine warm milk, yeast, and 1 tablespoon sugar in a small bowl. Allow to rest for 5 minutes until foamy.
02 - In a large mixing bowl, whisk together remaining sugar, eggs, melted butter, salt, and vanilla. Stir in the activated yeast mixture.
03 - Gradually add flour, stirring until a sticky dough forms. Transfer to a lightly floured surface and knead for 5 to 7 minutes until smooth and elastic.
04 - Place dough in a greased bowl, cover with a cloth, and allow to rise in a warm location until doubled in size, approximately 1 to 1.5 hours.
05 - Punch down the risen dough. Roll out on a floured surface to 1/2-inch thickness. Cut into 2-inch squares using a sharp knife or pastry cutter.
06 - Heat oil in a large, heavy-bottomed pot to 350°F.
07 - Fry beignets in batches without crowding, turning once, for 1 to 2 minutes per side until puffed and golden brown.
08 - Remove beignets with a slotted spoon and drain on paper towels.
09 - Generously dust warm beignets with powdered sugar immediately before serving.