Cut out 4 circles of puff pastry that are larger then the patties. Place a slice of cheese directly into the middle of the circle, then place the burger on top. Brush the surrounding pastry with beaten egg. Gather up the pastry around the burger patty and make sure it’s well sealed. Turn the burger upside down and place onto a lined baking sheet. Repeat with the other pastry circles, cheese and beef patties. Brush all over with the remaining egg and sprinkle with the sesame seeds. Bake for 25 minutes until the pastry is golden brown and cooked through.
Make the dipping sauce by mixing all of the ingredients together in a small bowl.
Serve each mini burger in a lettuce leaf, with a tomato slice on top, with a drizzle of burger sauce.