In a medium bowl, whisk together soy sauce, brown sugar, minced garlic, grated ginger, and sesame oil until fully combined.

Add the ground beef, mixing thoroughly to coat all of the meat with the marinade. Allow the beef to marinate for at least 1 hour in the refrigerator.

Remove beef from the refrigerator and divide it into equal portions. Shape each portion into round, flat patties, aiming for about ½ inch thick.

Preheat the grill to medium-high heat, about 400°F (200°C), and ensure the grill grates are clean and lightly oiled.

Grill the patties for approximately 5-7 minutes on each side, or until they reach your preferred doneness.

Slice the burger buns and lightly toast them on the grill until golden brown, about 1-2 minutes.

Assemble the burger by placing a grilled patty on the bottom bun and topping it with kimchi, lettuce, tomato, and cheese.

Place the top bun over the assembled burger and serve.