Drain block of tofu and wrap in a clean kitchen towel. Press with a plate or book for 10 minutes to remove extra liquid while you prepare the marinade.
Whisk together marinade ingredients in a wide dish or baking pan.
Cut pressed tofu into desired shapes. 1/2" steaks or 1" cubes work well. Toss cut tofu in the marinade to coat, then cover and set in the refrigerator for at least 30 minutes. (It's ideal to let this marinate for a few hours or overnight.)
Thread tofu cubes on skewers and grill, or grill tofu steaks directly on grill grates until slightly charred. You can also bake this tofu on a parchment-lined tray for 35-40 minutes at 400°F, flipping halfway. You can also pan-fry this tofu in a nonstick skillet or cast-iron until slightly charred; but note that the sugar in the marinade will caramelize quickly, so keep an eye on it and use medium heat.