Beat the softened cream cheese, sugar, and vanilla together until completely smooth, about 60 seconds with a hand mixer. Scrape the bowl and beat again briefly.
Unroll the crescent dough. Lay two triangles together with their long edges overlapping and pinch the seam closed to form a rectangle. Repeat to make four rectangles.
Spoon about 2 tablespoons of filling into the center of each rectangle, leaving a 1/2-inch border of bare dough all the way around.
Fold the two long sides up and over toward the center, leaving the filling exposed in the middle. Pinch the corners to seal.
Place on a greased air fryer tray or in a parchment-lined basket, spacing them apart so air can circulate. Work in batches if needed.
Air fry at 320°F for 6 to 8 minutes, checking at 5 minutes. If the bottoms look pale, flip them for the last 30 to 60 seconds.
Let cool 5 minutes before serving. The filling is very hot straight out of the air fryer.