In a large bowl, combine the beef mince, onion, salt, pepper, garlic powder, Worcestershire sauce, and grated cheese. Mix until just combined. Do not overmix.
Divide the mixture into 4 equal portions.
Gently slice the pitas open to create two thin rounds. You can microwave the pitas for around 30 seconds before slicing so that they soften, and are easier to slice.
Press one portion of the mince mixture into each pita half in an even layer, pressing it flat right to the edges. This is what creates the “smash burger” effect inside the pita.
Close the pita, then brush the top of each stuffed pita with the whisked egg and sprinkle with sesame seeds.
Air-fry at 180°C for 8 minutes, flipping halfway, until golden, crispy and cooked through. If meal-prepping, air-fry only the pitas you are eating now, and store the rest in an air-tight container to air-fry later.
Once hot and crispy, remove from the air fryer. Open slightly and add ketchup, and sliced gherkins.
Serve immediately while hot and crispy, with a side salad.