Place cottage cheese in piece of cheesecloth or fine-mesh strainer set over bowl. Press with plate or something heavy and let drain in fridge for at least 2 hours.

In mixing bowl, combine flour, baking powder and salt.

In separate bowl, beat eggs until frothy. Add sugar and vanilla and beat until light and fluffy. Beat in drained cottage cheese. Add flour mixture and stir until just combined.

Preheat air fryer to 320 degrees F. With wet hands, shape dough into roughly 2-tablespoon-sized balls. Arrange a batch of balls in air fryer basket, leaving at least one inch between each piece. Air fry for 8 to 10 minutes, turning halfway through, until golden and firm. Repeat with remaining dough.

Place melted butter in shallow dish. Roll hot donuts in butter and dust with powdered sugar.