In a medium bowl, combine the lukewarm milk, yeast, and 1 teaspoon granulated sugar, stir, and let stand for 5 to 10 minutes until foamy.

Whisk in the remaining 1/4 cup granulated sugar, salt, egg, and 1/4 cup melted butter until smooth.

Add the flour gradually, stirring until a soft dough forms, then knead on a lightly floured surface for 5 to 7 minutes until smooth, elastic, and slightly tacky.

Place the dough in a lightly greased bowl, turn once to coat, cover tightly with plastic wrap, and let rise in a warm place until doubled in size, about 1 hour.

Lightly flour a work surface, turn the risen dough out, gently punch it down, and roll it to 1/2 inch thickness.

Cut out 10 to 12 donuts using a 3 inch round cutter, then cut out centers with a 1 inch cutter to form donut holes, re-rolling scraps as needed.

Transfer the donuts and holes to lightly floured parchment paper, cover loosely with greased plastic wrap, and let rise until doubled and puffy, about 30 minutes.

Preheat the air fryer to 350°F and let it heat fully while the donuts finish rising.

Spray the air fryer basket lightly with oil spray, then carefully place a single layer of donuts in the basket with space between each.

Spray the tops of the donuts lightly with oil spray and air fry at 350°F for 4 minutes, flipping halfway if needed, until golden brown and cooked through.

Remove donuts to a wire rack and repeat with remaining donuts and holes, spraying the basket and tops with oil before each batch.

While the last batch cooks, whisk together 6 tablespoons melted butter, powdered sugar, vanilla, and hot water in a bowl until smooth and pourable.

While the donuts and holes are still hot, dip each one into the glaze using two forks to submerge and lift, letting excess drip back into the bowl.

Place glazed donuts on a wire rack set over a baking sheet and let sit for about 10 minutes until the glaze sets and hardens.