Preheat the air fryer to 350°F
Cut the bread in a crosshatch (diamond) pattern: cut several rows one inch apart diagonally, and then a set of marks perpendicular to the first ones - again one inch apart. Cut until you reach the crust but don't cut all the way through.
In a medium bowl, whisk together butter, olive oil, garlic, salt and parsley.
Use your fingers to open each crack and spread a teaspoonful of the butter mixture in it. I used a brush to do this. (Save about 1 tablespoon of the butter mixture for later.) Stuff each crack with a pinch of mozzarella cheese.
Wrap with foil and air fry for 15 minutes to melt the cheese.
Then, unwrap the garlic bread and brush the surface with the remaining butter mixture. Air fry for an additional 5-8 minutes, or until crusty.