Add warm milk, 2 tablespoons of sugar, and yeast to a large bowl and mix with a whisk. Let sit for 3-4 minutes to allow the yeast to activate.
After 5 minutes, whisk this mixture again. Add the salt, egg, vanilla, melted butter, and sugar to the mixture and mix thoroughly.
In a larger bowl, add half of the flour to the wet mixture and combine. Combine flour and the second half, and whisk flour until a slightly sticky dough forms.
On a floured surface, knead the dough for 3-4 minutes. Place this back into the bowl and cover it with plastic wrap, saran wrap, or a damp towel. Let sit at room temperature to rise for 2 hours.
Remove the risen dough and place it again on a floured surface.
Take a rolling pin and flour it before rolling out a rectangle of this dough, on a flat surface, to about ¼ inch thickness. Use a pizza cutter or knife to cut out 1x2 inch pieces of dough or cut them into square shapes or square pieces.
Spray the air fryer with cooking spray, or place parchment paper in the air fryer basket. Place the dough into the air fryer basket in a single layer, leaving plenty of space around the dough.
Brush the tops of the beignets with melted butter or spray with nonstick cooking spray. You can also brush with egg yolk; this will help you get the crispy exterior or a traditional fried beignet.
Air Fry the beignets; set air fryer to 350 degrees f, and cook for 8-10 minutes, flipping halfway during the cooking process.