Freeze the butter. Place the butter in the freezer for at least 15 minutes before preparing the biscuit dough.
Mix the dry ingredients. Add the flour, baking powder, sugar, and salt to a large mixing bowl. Add the shortening and use your hands to squeeze it into the flour until evenly incorporated.
Add the frozen butter. Grate the frozen butter over the flour mixture. Gently toss the grated butter into the flour with your hands until distributed throughout. Avoid pressing the butter into the flour.
Add the buttermilk. Pour in the buttermilk and mix until incorporated and a shaggy, sticky dough forms.
Shape the dough. Flour your work surface and turn the dough out onto it. Lightly dust the top with flour, then press the dough into a square about 1 inch thick.
Fold the dough. Lightly dust the dough with flour and fold it over itself like closing a book. Press it back out and repeat until you've completed three folds. Use only a small amount of flour between the layers.
Cut the biscuits. Keep the work surface floured to prevent sticking. Dip a biscuit cutter in flour, cut out the biscuits, and place them on parchment paper. Gently fold and flatten the remaining dough to about 1 inch thick, then continue cutting until you've used as much dough as possible. This recipe made 9 full biscuits with a small piece of dough left over.
Chill the biscuits. Refrigerate the cut biscuits for approximately 15 minutes.
Preheat the air fryer. Set the air fryer to 390°F. Arrange the chilled biscuits in the basket, leaving room between them to rise and expand. My basket held 4 biscuits at a time.
Air fry. Cook for 9 minutes without flipping, until the biscuits are golden brown and cooked through. Brush with butter if desired, then serve.