In a large mixing bowl, whisk together the all-purpose flour, baking powder, and kosher salt until evenly combined.
Cut the cold, cubed salted butter into the dry ingredients using a pastry cutter or fork until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining.
Pour in the cold buttermilk and gently stir just until a thick dough forms; do not overmix.
Turn the dough onto a lightly floured surface and knead it 6–7 times to bring it together, then pat or roll into a 1½-inch-thick circle.
Press a 2½-inch biscuit cutter straight down into the dough to cut biscuits. Re-shape scraps as needed, handling the dough gently.
Spray the air fryer basket with nonstick spray and arrange the biscuits at least 2 inches apart.
Air fry at 400°F for 8–10 minutes, or until the biscuits are golden brown and cooked through.
Brush the melted butter over the hot biscuits and serve.