Make the dough. In a large bowl, whisk together the flour, sugar, and salt. Add the Greek yogurt and stir until a shaggy dough forms. Turn out onto a floured surface and knead 5–6 times until smooth — don't overwork it.
Preheat and roll. Preheat the air fryer to 350°F. Roll the dough on a floured surface to just under ½ inch thick.
Cut the donuts. Cut with a 4-inch round cutter; use a 1-inch cutter for the donut holes. Re-roll scraps only once.
Prep the basket. Brush the basket and the tops of the donuts generously with melted butter. Arrange in a single layer with space between each.
Air fry. Cook at 350°F for 5–6 minutes (3–4 minutes for the holes), until golden and springy.
Make the glaze. While the donuts cook, whisk powdered sugar, milk, corn syrup, vanilla, and salt in a wide shallow bowl until smooth. Should coat the back of a spoon.
Glaze while warm. The moment the donuts come out, dip each side in the glaze. Transfer to a wire rack set over parchment to catch drips.
Let set. Wait 8–10 minutes for the glaze to set shiny and crackly — or eat one immediately, warm and dripping. Chef's privilege.