In a large bowl, whisk together the 1 1/2 cup self-rising flour, 2 tablespoons granulated sugar, and 1/2 teaspoon salt. Add the 1 1/2 cup Greek Yogurt and mix it until a dough forms. I like to use my hands for this.
Preheat the air fryer to 350 degrees F, air fryer setting. On a clean work surface lightly dusted with flour, roll out the dough until it is a little under 1/2 inch thick.
Cut the dough; I like to use a 4-inch cookie cutter, plus a smaller size to make the donut holes.
Brush the basket with the melted 4 tablespoons unsalted butter and place the donuts, not touching them into the basket. Brush with the butter. Air Fry for about 5-6 minutes (at 350 degrees F, air fryer setting) or until lightly golden brown. Repeat with the donut holes (same time and temperature)
While the donuts are air frying up, make the glaze/icing: To Make the Glaze/Icing: Mix the 1 cup powdered sugar, 2-3 tablespoons milk, and 1/2 teaspoon pure vanilla extract in a shallow bowl. You want the glaze to be thin yet thick enough o coat the donuts.
When the doughnuts are done cooking, immediately dip them into the glaze and coat them all over.
Place on a wire rack to cool.