Preheat an outdoor grill for medium-high heat, and oil the grate.
Mix the lamb, egg, oregano, sherry, vinegar, red pepper flakes, garlic, green onions, mint, cilantro, bread crumbs, salt, and pepper together in a mixing bowl.
With your hands until evenly blended. Form into five patties.
Cook on the preheated grill until the burgers are cooked to your desired degree of doneness, about 4 minutes per side for medium-rare.
Use the thermometer until it reads 70 degrees C. Serve the buns on a serving platter.