Bring 2 inches of water to boil in a 2-quart saucepan. Add Brussels sprouts, reduce heat, and simmer covered for 5 minutes. Add broccoli and cauliflower. Bring to a boil, then reduce heat. Cover and simmer for 2 minutes. Drain vegetables and immerse immediately in cold water.When vegetables are cooled, drain in a colander.
Wash mushrooms and trim stems, leaving mushrooms whole. Place all vegetables in a heavy-duty plastic bag.
Combine Teriyaki Sauce ingredients. Pour over vegetables and seal bag tightly. Let marinate for 1 hour, turning bag occasionally. Add tofu during last 10 minutes.
Spear vegetables and tofu in an alternating pattern on four 10- to 12-inch skewers. Lay skewers on a large, shallow baking pan. Brush generously with remaining sauce.
Bake at 400ᵒ F. for 10 to 12 minutes, basting once or twice with sauce. Meanwhile, toast sesame seeds in an ungreased skillet over medium heat until lightly browned, stirring constantly.
Spread toasted sesame seeds on a heat-proof plate. Roll skewered vegetables, hot from the oven, in seeds. Serve at once with rice or couscous.