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.