01 - Combine warm milk, sugar, and yeast in a small bowl. Let stand for 5-10 minutes until the mixture becomes foamy and fragrant.
02 - Whisk flour and salt together in a large mixing bowl. Add the yeast mixture along with egg, melted butter, and vanilla extract. Stir until a sticky, shaggy dough forms.
03 - Turn the dough onto a lightly floured surface and knead for approximately 5 minutes until smooth, elastic, and no longer sticky to the touch.
04 - Place the dough in a greased bowl, cover with plastic wrap or a clean towel, and let rise in a warm, draft-free area for 1 to 1.5 hours until doubled in volume.
05 - Punch down the risen dough and turn onto a floured surface. Roll to 1/2-inch thickness and cut into 2 1/2-inch squares using a sharp knife or pizza cutter.
06 - Pour vegetable oil into a deep pot or fryer and heat to 350°F. Use a kitchen thermometer to ensure accurate temperature.
07 - Carefully add 3-4 beignets to the hot oil. Fry for 2-3 minutes per side, turning once, until puffed, golden brown, and cooked through.
08 - Remove beignets with a slotted spoon and transfer to paper towels to drain excess oil for about 1 minute.
09 - Generously coat warm beignets with powdered sugar. Serve immediately while hot for the best texture and flavor experience.