Heat the grill to moderately high heat, place the rack about 4 inches from the flame.
In a small saucepan over medium heat, combine the soy sauce, water, and mirin and cook until the mixture begins to boil, 2 to 3 minutes.
Remove the pan from heat and whisk in the honey, ginger, garlic, sesame oil, and brown sugar. Whisk until the sugar is fully dissolved.
Brush the cabbage steaks with canola oil and sprinkle with salt and pepper. Start grilling the cabbage, turning occasionally, for 40 to 45 minutes or until tender.
Keep an eye on it and pierce it with a sharp knife to see it is tender. Once it starts getting tender, brush it liberally with the teriyaki mixture and continue to cook, turning once or twice and brushing with more of the sauce, until it’s browned, 3 to 5 minutes.
Drizzle the cabbage with any remaining teriyaki sauce, and serve it immediately with lemon wedges on the side.
Garnish with sesame seeds and chopped green onions.