In a medium bowl, whisk together the gluten-free flour, baking powder, 1/2 cup sugar, and 1/4 tsp salt until well combined.

In a separate bowl, whisk the eggs, 3/4 cup milk, 2 tsp vanilla bean paste, and melted 3 tbsp butter until smooth.

Pour the wet ingredients into the dry ingredients and whisk just until a smooth batter forms; let the batter rest for 5 to 10 minutes to hydrate and thicken.

While the batter rests, make the pastry cream: in a small bowl whisk the egg yolks, 1/4 cup sugar, cornstarch, and 1/8 tsp salt until smooth and pale.

In a small saucepan, heat 1 cup milk over medium heat until steaming but not boiling, then slowly whisk it into the yolk mixture.

Return the mixture to the saucepan and cook over medium heat, whisking constantly, until thick and bubbling, 2 to 3 minutes.

Remove from heat, whisk in 1 tsp vanilla bean paste and 1 tbsp butter until silky, then transfer to a shallow bowl.

Press plastic wrap directly on the surface of the pastry cream and chill in the refrigerator until cold and spoonable.

Preheat the air fryer to 360 °F for 3 to 5 minutes, then lightly grease the basket with nonstick spray or neutral oil.

Spoon or pipe the rested batter into 12 even mounds in the air fryer basket, leaving space between each donut so they can puff.

Air fry the donuts in batches at 360 °F for 6 to 8 minutes, or until puffed, with golden edges and centers that spring back when lightly pressed.

Transfer cooked donuts to a wire rack and let them cool completely to room temperature.

While the donuts cool, make the chocolate glaze: in a small saucepan combine chocolate chips, heavy cream, 2 tbsp butter, and corn syrup.

Warm the glaze over low heat, stirring constantly, until the chocolate is melted and the mixture is smooth and glossy; remove from heat and let cool slightly until thick but still pourable.

To fill the donuts, poke a small hole in the side of each cooled donut with a skewer or small knife.

Transfer the chilled pastry cream to a piping bag fitted with a small round tip and pipe cream into each donut through the hole until the donut feels slightly heavy and you feel resistance.

Dip the top of each filled donut into the warm chocolate glaze, let excess drip back into the pan, then place the donuts back on the wire rack.

Let the glazed donuts stand at room temperature for 10 to 15 minutes, or until the chocolate is set, then serve.