In a bowl, combine the water, soy sauce, lime or lemon juice, ginger, sesame seeds, garlic, and scallions. Whisk well.
Put the cut tofu into a shallow dish, cover the the marinade, and let sit for 10-30 minutes (or up to overnight). Flip the tofu a few times throughout so that the marinade is absorbed evenly.
Preheat the oven to 400 degrees F. Place the marinated tofu pieces on a non-stick or parchment paper-lined baking sheet, allowing plenty of space between the pieces. Set any extra marinade aside.
Bake tofu for 20-45 minutes, depending on how firm you like it. Flip tofu over after about 15 minutes, and continue baking until done.
Meanwhile, heat a small wok or stir fry pan over medium heat. Add the sesame oil and once hot, add the baby bok choy stems, broccoli, and carrots; mix well. Cover the pan (to retain moisture), and stir fry for about 5 minutes or until tender. Turn off the heat, add the bok choy leaves and any extra ginger marinade. Stir until the leaves have wilted and everything is well combined.