In a small bowl, mix together the mayo, ketchup, yellow mustard, garlic powder, and paprika. Stir well and set aside.
Divide 1 pound of ground beef into 4 equal balls. Flatten each into thin patties, slightly wider than your bun, and season both sides with salt and pepper.
Preheat your air fryer temperature to 375 degrees F, for 3-5 minutes. Place the patties into the air fryer basket (in a single layer) and set cook time for 6-8 minutes, flipping halfway through. In the last minute, add a slice of cheese on top of each patty and cook until melted.
Lightly butter the inside of the potato buns and air fry them for a minute or until golden and warm.
Spread ShackSauce on the top and bottom buns. Add lettuce, tomato, and the cheesy burger patty. Top with the other bun and serve hot!