01 - Combine warm water, 1 tablespoon of sugar, and yeast in a small bowl. Stir gently and let sit for 5-10 minutes until mixture becomes foamy and fragrant.
02 - Whisk together milk, remaining sugar, egg, softened butter, and vanilla extract in a large mixing bowl until fully incorporated. Add the activated yeast mixture and stir to combine.
03 - Gradually incorporate flour and salt into the wet mixture, mixing until a sticky, cohesive dough forms. Ensure all dry ingredients are fully absorbed.
04 - Turn dough onto a lightly floured surface and knead for approximately 5 minutes until smooth, elastic, and no longer sticky to the touch.
05 - Place dough in a greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm, draft-free area for about 2 hours or until doubled in bulk.
06 - Punch down risen dough and roll out on a lightly floured surface to 1/4-inch thickness. Cut into 2 1/2-inch squares using a sharp knife or pizza cutter.
07 - Heat oil in a deep fryer or heavy pot to 350°F. Fry beignets in batches of 3-4, turning occasionally, until puffed and golden brown on both sides, approximately 2-3 minutes per batch.
08 - Remove beignets with a slotted spoon and drain briefly on paper towels. Generously dust with powdered sugar while warm and serve immediately for best texture.