Put the cucumbers into a large bowl and add the vinegar, soy sauce, sesame oil, honey and half the Korean chili flakes. Stir to combine. Taste and season with salt and more chili flakes to personal taste. Cover and set aside in the fridge until ready to use.
Put all the sauce ingredients in a blender or food processor and blend until smooth.
Toast the buns in a toaster or under the broiler for 3 minutes. Mix the mayonnaise and Sriracha in a small bowl and spread some mayo over the top and bottom buns.
Preheat a large nonstick or cast-iron pan over medium heat with a little vegetable or peanut oil. Add the burgers to the pan and cook about 5 minutes until you see the juices rising to the top of the burger.
Flip the burgers and pour the sauce over the burgers. Spread the sauce in the pan and allow the sauce to simmer along with the burgers. Top with the slices of cheese and continue to simmer and move the burgers around in the pan. As the burgers finish cooking, the sauce will thicken and cling to the bottom and sides of the burger.
Put the burgers onto the bottom buns directly from the pan. Top with some cucumbers, and sprinkle with the sliced scallions and sesame seeds. Top with the top bun and serve.