In a large mixing bowl, combine 2 cups of flour, sugar, salt, and instant yeast.
Add warm milk, melted butter, and egg to the dry ingredients. Mix until combined.
Gradually add the remaining flour, mixing until the dough starts to form. You may need slightly more or less flour.
On a lightly floured surface, knead the dough for about 6-8 minutes until it's smooth and elastic.
Place the dough in a greased bowl, cover it, and let it rise in a warm place until doubled in size, about 1 hour.
Punch down the risen dough and turn it out onto a lightly floured surface.
Divide the dough into 12 equal pieces and shape each into a ball.
Arrange the dough balls in a parchment-lined air fryer basket, leaving space between each for expansion. You may need to cook in batches depending on the size of your air fryer.
Cover the rolls in the air fryer basket with a clean kitchen towel and let them rise for another 30 minutes.
Preheat the air fryer to 320°F (160°C) for 3 minutes.
Place the basket in the air fryer and cook the rolls for about 5-7 minutes, or until they are golden brown and cooked through.
Brush the hot rolls with additional melted butter if desired for a glossy finish and softer crust.
Serve the rolls warm as a side for your favorite meals.