1Line the air fryer with parchment paper, grease with oil, and place the burger patties on top. Season with oil and pepper, then bake at 200-205°C for 6 minutes. Let the cooked patties rest for 5-10 minutes.
2Combine Greek yogurt, ketchup, sliced pickles, French mustard, and regular mustard in a deep bowl and mix until smooth.
3Place processed cheddar cheese in the center of a puff pastry flatbread, add some sauce, the cooked beef patty, more sauce, diced potatoes, red onion, and tomato slices. Top with cheddar cheese, then fold and crimp the edges of the flatbread to seal.
4Place the assembled burgers onto parchment paper in the air fryer, brush with butter, and sprinkle with sesame seeds. Bake at 180°C for 15 minutes.
5Serve the finished burgers on a plate with fresh lettuce leaves.