In a medium bowl, whisk flour, baking powder, and salt.
In a large bowl, whisk melted butter, sugar, buttermilk, egg, sour cream, and vanilla until smooth.
Add dry ingredients to the wet mixture and stir gently until just combined.
Toss frozen blueberries with 1 tablespoon flour, then fold into the dough.
Cover and refrigerate the dough for 30 minutes.
Roll chilled dough into 1-tablespoon portions and place on a parchment-lined tray.
Preheat air fryer to 350°F (175°C).
Line basket with parchment and arrange donut holes in a single layer.
Air fry 8–10 minutes, flipping halfway, until golden.
For the glaze, whisk powdered sugar, milk, and strained blueberry puree.
Dip warm donuts in glaze and let set before serving.