In a large chilled mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, sugar, and salt to ensure even distribution of leavening agents.
Incorporate the cold cubed butter into the dry ingredients using a pastry blender or two knives until the mixture resembles coarse meal with pea-sized butter chunks remaining.
Create a well in the center and pour in the cold buttermilk. Stir gently with a fork until a shaggy dough just begins to form; do not overmix to prevent gluten development.
Turn the dough onto a lightly floured surface and pat into a rectangle. Perform 5 letter-folds (folding the dough over itself) to create structural laminations for flakiness.
Flatten the dough to a consistent 1-inch thickness. Use a 2.5-inch circular cutter to stamp out biscuits, pressing straight down without twisting to avoid sealing the edges.
Preheat the air fryer to 330°F (165°C).
Arrange the biscuit rounds in the air fryer basket in a single layer, ensuring they are not touching for optimal airflow or slightly touching for a higher vertical rise.
Air fry at 330°F for 10 to 12 minutes until the internal temperature reaches approximately 200°F and the tops are golden brown.
Immediately brush the surfaces with melted butter upon removal from the air fryer.