01 - Combine warm milk, yeast, and 1 tablespoon sugar in a small bowl. Allow mixture to sit undisturbed until foamy, approximately 5 minutes.
02 - In a large mixing bowl, whisk together remaining sugar, eggs, melted butter, salt, and vanilla extract. Stir in the activated yeast mixture until combined.
03 - Gradually add flour to wet ingredients, stirring until a sticky dough forms. Transfer dough to a lightly floured surface and knead for 5 to 7 minutes until smooth and elastic.
04 - Place dough in a greased bowl and cover with a damp cloth. Allow to rise in a warm location until doubled in volume, approximately 1 to 1.5 hours.
05 - Punch down risen dough. On a floured surface, roll dough to 1/2-inch thickness. Cut into 2-inch squares using a sharp knife or pastry cutter.
06 - Heat vegetable oil in a large, heavy-bottomed pot or deep fryer to 350°F.
07 - Working in batches, carefully place beignets into hot oil. Turn once and fry until puffed and golden brown, approximately 1 to 2 minutes per side. Avoid overcrowding the pot.
08 - Remove fried beignets with a slotted spoon and drain on paper towels. Generously dust warm beignets with powdered sugar immediately before serving.