Bring a large pot of water to a boil and prepare an ice bath in a separate bowl.
Blanch the cabbage leaves in the boiling water for 2 minutes until pliable, then immediately transfer to the ice bath to stop the cooking and pat dry.
Finely chop the shiitake mushrooms and mince the garlic and ginger.
In a mixing bowl, combine the ground beef, chopped mushrooms, garlic, ginger, half of the sliced green onions, sea salt, and black pepper.
Lay each cabbage leaf flat, place a portion of the beef mixture at the base, fold in the sides, and roll tightly like a burrito.
Place the rolls in a steamer basket over simmering water, cover, and steam for 12-15 minutes until the beef is cooked through.
In a small bowl, whisk together the tamari, toasted sesame oil, and rice vinegar.
Serve the hot cabbage rolls drizzled with the tamari glaze and garnished with the remaining green onions.