01 - Combine warm milk, sugar, and yeast in a small bowl. Let stand for 5-10 minutes until mixture becomes foamy, indicating the yeast is active.
02 - Whisk flour and salt together in a large mixing bowl. Add the yeast mixture, egg, melted butter, and vanilla extract. Mix until a sticky dough forms.
03 - Turn dough onto a lightly floured surface and knead for approximately 5 minutes until smooth and elastic in texture.
04 - Place 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 size.
05 - Roll risen dough to 1/2-inch thickness on a floured surface. Cut into 2 1/2-inch squares using a sharp knife or pizza cutter.
06 - Heat vegetable oil in a deep pot or fryer to 350°F. Maintain temperature throughout frying for consistent results.
07 - Fry 3-4 beignets at a time for 2-3 minutes per side, turning once, until puffed and golden brown on both sides.
08 - Remove beignets with a slotted spoon and drain on paper towels to remove excess oil.
09 - Generously dust warm beignets with powdered sugar. Serve immediately while still warm for the best texture and flavor.