Whisk together flour, baking powder, baking soda, salt, and sugar in a large bowl.
Add cold butter cubes. Work into the flour using a pastry cutter or fingertips until pea-sized pieces form. (Or grate frozen butter directly into flour.)
Pour in cold buttermilk. Fold until the dough just comes together — it should look shaggy, not smooth.
Turn onto a lightly floured surface. Press into a ¾-inch rectangle. Cut into 4 pieces and stack. Press down and repeat the fold once more.
Press to a final ¾-inch thickness. Cut with a 2–2.5 inch round cutter, pressing straight down without twisting.
Place biscuits on a plate and refrigerate for 10 minutes.
Arrange chilled biscuits in a single layer in the air fryer basket, leaving ½ inch of space between each.
Air fry at 325°F (165°C) for 13–15 minutes until golden brown on top and set on the sides. Do not flip.
Brush immediately with melted butter. Serve warm.