Place the flour, baking powder, cream of tartar, sugar, and salt in a large bowl. Cut the cold butter into small cubes or grate it, then add it into the bowl.
Using your fingers or a pastry cutter, work the butter into the flour until you have small, pea-sized crumbs. The key here is to keep the butter cold so the biscuits turn out flaky. If the butter starts melting, pop the bowl into the fridge for a few minutes.
Slowly add the cold yogurt to the flour mixture, stirring gently with a fork or spatula until the dough just comes together. Be careful not to overmix, as this can make the biscuits tough.
Turn the dough out onto a floured surface and gently knead it a few times to bring it together. Then, roll or pat the dough out to about 1-inch thickness. Using a biscuit cutter (or the rim of a glass), cut out your biscuits. Gather the scraps, re-roll, and cut out more biscuits until the dough is used up.
Place the biscuits in the air fryer basket in a single layer, making sure they’re not touching. Depending on the size of your air fryer, you may need to do this in batches. Cook the biscuits at 380°F (195°C) for 8-10 minutes, or until they’re golden brown and cooked through.
Once the biscuits are done, remove them from the air fryer and brush the biscuits with a little melted butter.
Let them cool for a couple of minutes before serving. They’re best enjoyed warm, but they also reheat beautifully if you want to save some for later.