Step 1

Combine milk, yeast and 1 tablespoon granulated sugar in a measuring cup. Let stand until foamy, about 5 minutes. Pour the yeast mixture into the bowl of a stand mixer fitted with a dough hook attachment. Add flour, salt and the remaining 5 tablespoons granulated sugar. Beat on low speed until combined, about 30 seconds. Whisk egg, egg yolk, vanilla and 4 tablespoons melted butter together in a measuring cup or small bowl until combined. With the mixer running on low speed, gradually add the egg mixture to the flour mixture. Increase speed to medium-high and beat until the dough forms a loose ball around the hook and is smooth and elastic, about 3 minutes.

Step 2

Place the dough on a lightly floured surface and knead, adding a little more flour, if needed, until it forms a smooth ball. Transfer to a lightly greased large bowl. Cover loosely and let rise in a warm draft-free place (80-85°F) until doubled in size, about 1 hour.

Step 3

Turn the dough out onto a lightly floured work surface. Roll out into a 10-inch square; cut into 20 rectangles. Cover lightly with a kitchen towel and let stand for 15 minutes.

Step 4

Preheat air fryer to 350°F for 5 minutes. Lightly coat the basket with cooking spray. Add 4 to 6 dough pieces to the basket, placing them 1/2 inch apart. Coat the dough pieces lightly with cooking spray. Cook until golden brown, 3 to 4 minutes. Turn the beignets over, coat with cooking spray and cook until the other side is golden brown, 3 to 4 minutes more. Brush the beignets with some of the remaining melted butter. Transfer to a serving platter and immediately dust with confectioners' sugar. Repeat with the remaining dough pieces.