In a small bowl, gently stir together the blueberries, granulated sugar, flour, and crumbled goat cheese. Leave the goat cheese in visible crumbles.
Unroll the pie dough onto a lightly floured surface. Cut out circles with a 3-inch biscuit cutter, re-rolling the scraps once to reach 12 rounds.
Spoon about 1 tablespoon of filling onto one half of each round, leaving a 1/2-inch border clear.
Dampen the border with water, fold the dough over into a half-moon, and press the edges together. Crimp the seam with the tines of a fork.
Cut two small vents in the top of each empanada.
Brush the tops with beaten egg and sprinkle with turbinado sugar.
Preheat the air fryer to 350°F.
Place the empanadas in a single layer in a greased basket or on perforated parchment, leaving space between each. Air fry for 9 to 11 minutes, until deep golden and puffed. Work in batches.
Rest 5 minutes before serving. The filling is very hot.