Whisk all the marinade ingredients together in a bowl. Set aside.
Unwrap the tofu (if you pressed it) and cut into 1 to 1½ inch cubes (I err on the bigger side for skewers). Place the tofu in a rectangular container with a tight-fitting lid. Pour the marinade over the tofu and place in the fridge for 6 hours (you can even go overnight), flipping the container 2 to 4 times throughout for even marinating.
Preheat the oven to 400ºF and line a baking sheet with parchment paper.
Thread the tofu and zucchini onto each skewer. I like to do three pieces of tofu and two to three zucchini per skewer. Reserve the leftover marinade. Lay the skewers on the baking sheet.
Bake for 20 minutes, rotate, baste again with the marinade (still reserving the leftovers), and bake for another 15 to 20 minutes until the tofu is firm and maybe even a little charred on the edges.
When there are a few minutes left on the skewers, pour the leftover marinade into a small pot and bring to a gentle simmer. In a separate small bowl, whisk together the arrowroot starch and 2 tablespoons of water (this will help thicken the marinade) and stir this into the simmering marinade. Simmer for another couple of minutes until the mixture thickens. Remove from heat.
Remove the skewers from the oven. Baste generously with the hot, thickened marinade, garnish with herbs or green onion, and serve!