Lay eggplant rounds on a work surface. Cut a small slit horizontally through each round, making a pocket to form 'burger buns' that are still joined together.
Mix pork, 2 tablespoons tamari, green onions, ginger, salt and black pepper together in a bowl. Stuff mixture into the 'buns.'
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add the stuffed buns and cover. Steam until tender and pork is only slightly pink in the centre, about 20 minutes.
Make dipping sauce
Mix 1/4 cup tamari, garlic, sesame oil and vinegar together in a small bowl to make the dipping sauce. Serve with the cooked eggplant burgers.
Apple cider or white wine vinegar both work in this recipe.