Preheat the grill to medium heat, approximately 375–400°F, and lightly oil the cooking grate.
Divide the beef into six equal 4-ounce (113 g) portions. Gently form the portions into patties and season both sides evenly with the meat tenderizer, kosher salt, and black pepper.
Melt the butter in a 10-inch skillet over medium heat. Add the drained mushrooms and soy sauce. Cook for 5–7 minutes, stirring periodically, until the watery liquid evaporates and the mushrooms show light browning. Keep warm.
Grill the patties for 2–4 minutes on the first side. Turn once and cook for another 2–4 minutes, continuing as necessary until each patty reaches 160°F/71°C in the center.
Divide the warm mushroom mixture among the patties on the grill. Top each with one Swiss cheese slice, close the lid, and cook for approximately 1 minute, until the cheese melts.
Transfer the patties to a clean platter. Place each patty on a hamburger bun and serve immediately.