In a medium bowl, cream together the softened unsalted butter and granulated sugar with a hand mixer until light and fluffy, about 2 minutes. Beat in the egg yolk, vanilla extract, and almond extract until smooth.
Add the all-purpose flour, baking powder, and salt to the butter mixture. Mix on low speed until a soft dough forms. Do not overmix - stop as soon as no dry flour remains.
Scoop the dough into tablespoon-sized portions and roll into smooth balls. Gently press each ball down to about 1/2-inch thickness. Sprinkle the tops with coarse sugar, pressing it in lightly.
Preheat the air fryer to 300 degrees F. Cut a piece of parchment paper to fit the air fryer basket. Place the cookies on the parchment about 1 inch apart - you will likely need to bake in 2 to 3 batches.
Air fry at 300 degrees F for 7 to 8 minutes, until the edges are just barely turning golden. The centers may look slightly underdone - that is perfect.
Let the cookies cool in the air fryer basket for 2 minutes, then transfer to a wire rack to cool completely. They will firm up as they cool into perfectly soft, buttery sugar cookies with a lightly crisp edge.