Press 1/2 cup white sugar and butter together in a bowl until crumbly. Add egg yolks and stir until well combined.
Sift flour, baking powder, and salt into a separate bowl. Place 1/3 of the flour mixture and 1/2 the sour cream into the sugar-egg mixture; stir until combined. Mix in the remaining flour and sour cream. Refrigerate dough until ready to use.
Mix 1/3 cup sugar and cinnamon together in a bowl.
Roll dough out onto a lightly floured work surface to 1/2-inch thick. Cut 9 large circles in the dough; cut a small circle out of the center of each large circle to create doughnut shapes.
Preheat an air fryer to 350 degrees F (175 degrees C).
Brush 1/2 of the melted butter over both sides of the doughnuts.
Place 1/2 doughnuts into the basket of the air fryer; cook for 8 minutes. Paint cooked donuts with the remaining melted butter and immediately dip into the cinnamon-sugar mixture. Repeat with the remaining doughnuts.
Cook time may vary by the strength and capacity of your air fryer; check and adjust accordingly.
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