In a small bowl, stir together the hoisin, soy sauce, teriyaki sauce, sriracha, rice vinegar, and sesame oil. Set aside.
Press the tofu between paper towels to squeeze out as much liquid as possible. Refresh the paper towels and press again.
Heat the 2 teaspoons canola oil in a large nonstick skillet over medium-high. Once the oil is hot, crumble in the tofu, breaking it into very small pieces as it cooks.
Continue cooking for 5 minutes, then add the diced mushrooms. Continue cooking until any remaining tofu liquid cooks off and the tofu starts to turn golden, about 3 minutes more.
Stir in the water chestnuts, garlic, ginger, red pepper flakes, and half of the green onions and cook until fragrant, about 30 seconds more.
Pour the sauce over the top of the mixture and stir to coat. Cook just until it's bubbling and the sauce is warmed through, about 1 minute.
Spoon the tofu mixture into individual lettuce leaves. Top with remaining green onions and grated carrots.
Serve and enjoy!