Pat dry the wings and line in a single layer on a tray.
Preheat the air fryer to 390 degrees F.
Combine the dry rub ingredients: paprika, chili powder, oregano, garlic powder, onion powder, salt, pepper and mesquite. Dust both sides of each wings in the rub. Toss the wings in a bit of cornstarch to get them cooking nice and crispy.
Pour a touch of water in the air fryer under the basket and spray the basket of the air fryer with a bit of cooking oil. Layer wings in a single layer and cook 10 minutes per side. Repeat until all the wings are cooked.
For the garlic parmesan sauce: In a saucepan combine butter with minced garlic cloves over medium heat. Once the butter is melted and begins to bubble add the oregano, thyme, salt, pepper and chili powder. Stir in the sugar, water and parmesan cheese until the cheese is all melted and well incorporated. The mixture should be a little thick. Remove from heat and combine with the mayonnaise.
Add the wings to a large shallow mixing bowl, pour the garlic parmesan sauce overtop and toss until well coated.
Serve immediately with chopped parsley and extra parmesan cheese.