Combine the shredded cabbage, grated carrots, jalapeño, chopped cilantro, minced ginger, lime zest, salt, and sugar in a large mixing bowl. Toss these ingredients together until well combined. Drizzle fresh lime juice over the mixture, stirring gently to incorporate. Cover the bowl and refrigerate for at least 10 minutes.

In a small bowl, whisk together soy sauce, mirin, sake, and sugar until dissolved. Set this sauce aside for later use.

Slice the tofu into thick slabs and score the top in a crosshatch pattern. Marinate the tofu in soy sauce for 5 minutes. Mix cornstarch with garlic powder and thyme in a shallow dish, and dredge tofu slabs in this mixture.

Heat oil in a skillet over medium heat. Add the coated tofu and sear for about 5 minutes on each side until golden brown.

Pour the teriyaki sauce over the seared tofu and cook for an additional 2–3 minutes, allowing the sauce to thicken and coat the tofu.

Assemble the sandwich by spreading sriracha mayo on bread, layering on avocado slices, glazed tofu, and slaw. Top with another slice of bread or bun.