Divide beef into two 3-ounce balls. Lightly moisten fingertips with water and press beef into patties about 1/4-inch thick. Drop Worcestershire sauce over patties; rub in lightly. Sprinkle garlic powder, black pepper, salt, and cayenne on top and rub in.
Cut a circle of cheese using a pastry cutter or the rim of a glass. Place cheese onto 1 patty; cover with the other patty. Press edges together carefully. Flip and continue pressing until fully sealed. Season both sides with a little salt.
Heat a cast iron skillet over medium-high heat. Cook patty for 5 minutes per side for medium doneness. Place patty on one half of a bun. Top with tomato, lettuce, and the other half of the bun.