In a large bowl, combine the warm milk, yeast, and a pinch of the granulated sugar. Stir gently and let it sit for about 8 to 10 minutes until the mixture becomes foamy and bubbly, which tells you the yeast is active.
Whisk the egg, melted butter, vanilla extract, and remaining granulated sugar into the yeast mixture until smooth. Gradually add the flour and salt, stirring with a wooden spoon until a soft, slightly sticky dough forms.
Turn the dough out onto a lightly floured surface and knead for about 3 to 4 minutes until it is smooth and elastic. Place the dough in a lightly greased bowl, cover with a clean kitchen towel or plastic wrap, and let it rise in a warm spot for about 1 hour or until doubled in size.
Once risen, punch the dough down gently. Roll it out on a floured surface to about 1/4-inch thickness. Cut the dough into roughly 2-inch squares using a sharp knife or pizza cutter. You should get about 20 to 24 pieces.
Preheat your air fryer to 350 degrees F. Lightly spray the air fryer basket with cooking spray. Working in batches to avoid crowding, place the beignets in a single layer with a little space between each one. Spray the tops lightly with cooking spray.
Air fry for 4 minutes, then carefully flip each beignet and cook for another 3 to 4 minutes until they are puffed up and golden brown all over.
Transfer the hot beignets to a plate and immediately dust them very generously with powdered sugar on all sides. Repeat with the remaining dough. Serve right away while warm and pillowy.