To make the dough, begin by combining yeast, 1 tablespoon of granulated sugar, and the milk in the bowl of a stand mixer. Set aside for at least 5 minutes.
Meanwhile, melt the butter in a small bowl and combine well with the eggs and the vanilla
Add the rest of the granulated sugar, the flour, and salt to the yeast mixture.
Beat on low speed for about 1 minute until just incorporated then drizzle in the egg and butter mixture.
Continue beating on medium speed for about 4 minutes until an elastic and smooth dough forms.
Form the dough into a ball and place it into a large bowl that has been lightly greased. Cover and let the dough rise for about 1 hour or until doubled in size.
Preheat the air fryer to 350 degrees F / 180 degrees C.
Transfer the dough to a lightly floured surface and roll it to a quarter-inch thick.
Cut the dough with a round cookie cutter. You can also slice into rectangles using a sharp knife or pizza cutter.
Coat the air fryer basket with cooking spray and add the beignets to the air fryer. Leave space between the beignets and coat them with melted butter or canola spray.
Air fry the beignets for 4 minutes, turn and cook for an additional 4 minutes, or until golden brown.
Place the beignets on a cooling rack. Brush the warm pastries with more melted butter, then dust with powdered sugar.