Heat up a small saucepan with low heat and combine the lime juice, garlic, ginger, maple syrup, 1/4 cup of water, tamari, and mirin in order to make the tamari-ginger glaze. Bring the ingredients to boil and allow to simmer for 5 minutes.
While you’re preparing the tamari-ginger glaze simultaneously mix the cornstarch and 2 teaspoons water in a very small bowl and whisk them for 60 seconds. Afterward, pour the cornstarch mixture into the tamari mixture in the saucepan and cook it until it becomes a thick and syrup-like sauce (this should only take about 1 minute). Transfer the mix from the saucepan into a clean small bowl and let cool.
Preheat the teppanyaki grill.
Use a water bottle spray and put cooking oil inside to spray the teppanyaki grill surface with oil in order to prevent the vegetables from sticking to it. Add the vegetables to one side of the teppan and the tofu next to it (or use two separate pans if your using skillets). Place a lid to cover the tofu and allow to cook turning once to cook each side for about 5-6 minutes.
Once all sides have a brownish tint, then transfer the tofu into a sheet pan and brush them with the tamari-ginger glaze that you’ve prepared earlier. Then add some sesame seeds.
Add salt and pepper to taste to the vegetables and serve alongside the tofu with some steamed rice.
Serve as is or you may choose to add one or more Japanese sauces to satisfy your taste.