Place the shrimp in a food processor and pulse until coarsely chopped but not pureed.
In a large bowl, combine the chopped shrimp, panko breadcrumbs, egg, minced garlic, parsley, Old Bay seasoning, salt, and black pepper. Mix well until all ingredients are fully incorporated.
Divide the shrimp mixture into 4 equal portions and shape each into a patty about 3 inches in diameter and 1/2 inch thick.
Preheat the air fryer to 375°F (190°C) for 3 minutes.
Lightly spray the air fryer basket with cooking spray to prevent sticking.
Place the shrimp patties in the air fryer basket in a single layer without overlapping.
Cook the patties for 5 minutes, then carefully flip them and cook for an additional 5 minutes or until the shrimp burgers are golden brown and cooked through.
While the patties cook, mix the mayonnaise and Dijon mustard in a small bowl to make the sauce.
Lightly toast the hamburger buns in a toaster or on a skillet until golden brown.
To assemble the burgers, spread the mayo-mustard sauce on the bottom half of each bun, add a leaf of romaine lettuce, a shrimp patty, a slice of tomato, and then top with the bun.
Serve immediately and enjoy your air fryer shrimp burger.