2. Combine the ingredients for the marinade in a mixing bowl and whisk to mix. Pour the marinade over the tofu. Marinate in the refrigerator for 1 to 2 hours, turning the tofu pieces several times so they marinate evenly.
3. Strain the marinade into a saucepan and bring to a boil. Briskly simmer the marinade uncovered until reduced to a thick, syrupy glaze, 5 to 10 minutes.
4. Set up your grill for direct grilling and preheat to high. Brush and oil the grill grate. Skewer the tofu pieces through the narrow end, 2 skewers per piece. Arrange the resulting kebabs on the grate. Grill the tofu until sizzling and well browned, 4 to 6 minutes per side. (Protect the skewers with strips of foil if they start to burn.) Baste the tofu with the glaze as it cooks.
5. Transfer the tofu to plates or a platter and drizzle with any remaining glaze. Sprinkle with the sesame seeds and reserved scallion greens and serve at once.