1. Whisk together the vinegar, hoisin sauce, soy sauce, sesame oil and crushed red pepper in a small bowl and set aside.
2. Cut the tofu in half horizontally. Wrap the tofu halves in paper towels and press down firmly to remove excess moisture. Crumble the tofu into small pieces. Heat the canola oil in a large nonstick skillet over medium-high heat. Add the crumbled tofu and cook, stirring and breaking it into smaller pieces, until it starts to brown, about 5 minutes. Add the mushrooms and continue cooking and stirring until all the liquid has evaporated, about 3 minutes. Stir in the daikon, garlic, ginger and scallions. Add the reserved sauce and cook until well combined and heated through, about 2 minutes.
3. Spoon about 1/2 cup of the tofu mixture into each lettuce leaf. Top with shredded carrots if desired.