To activate the yeast, in a small bowl, use a whisk to combine together the water, milk, yeast, and sugar. Set this aside until the yeast has bloomed (you will see foam in about 10 minutes).
In a mixing bowl combine together the flour, salt, activated yeast, and melted butter. When the ingredients start to stick together, roll the dough into a large ball, place it into the bowl (you can grease the bowl first) and then place a clean kitchen tea towel over the bowl and place the mixture in a warm place to rise.
Once the dough has doubled in size (about an hour and a half) you can take it out of the bowl and on a clean work space that has been dusted with flour, gently knead the dough.
Roll the dough back into a ball and then use a knife to slice it into four quarters and then slice each of the quarters into halves so that you have eight pieces of dough that are approximately the same size.
Line your air fryer basket with parchment paper. Roll each piece of dough into a ball and place it into the air fryer basket on top of the parchment paper. Place the basket into the air fryer, which will stay off, and allow the rolls to rise for 45 minutes in the air fryer.
After the 45 minutes has passed, use a pastry brush to brush the tops of each of the rolls with the beaten egg.
Set your airfryer to 300 and air fry the rolls for 12 minutes. Check the rolls and continue to air fry until the rolls turn golden on top (about 15 minutes total air fry time).
Carefully remove the rolls from your air fryer and serve.