Step 1

Combine the flour, sugar, yeast and salt in the bowl of a stand mixer fitted with the dough hook and mix to combine. Add the egg, egg yolk, milk, butter and vanilla and mix on low to combine. Increase the speed to medium high and knead until the dough forms a loose ball around the hook and is smooth and elastic, about 3 minutes.

Step 2

Transfer the dough to a floured surface and lightly knead by hand just enough to bring it together into a smooth ball. Brush a medium bowl with melted butter and add the dough, turning to coat. Cover and let rise in a warm area until doubled in size, 1 hour to 1 hour 15 minutes.

Step 3

Punch the dough down and roll out on a lightly floured surface to a square slightly larger than 10 inches by 10 inches. Trim the edges with a sharp knife or pizza cutter to make an even square. Cut the square in a 4 by 5 grid pattern to make 20 rectangles. Loosely cover the dough and let rise right on the countertop for about 15 minutes.

Step 4

Preheat a 3.5-quart air fryer to 350 degrees F. Spray the basket with cooking spray and add half the beignets. Spray the beignets lightly with cooking spray. Cook until puffed and golden, about 6 minutes. Remove and repeat with the remaining beignets. Dust the beignets with confectioners' sugar and serve warm.