Lettuce Wraps with Mushrooms and Tofu

Name: Lettuce Wraps with Mushrooms and Tofu
Ingredients: 1 cup seasoned rice vinegar; 1 tablespoon granulated sugar; 4 Persian cucumbers, sliced into thin rounds; 16 ounces shiitake mushroom caps; 1 shallot, roughly chopped; 1/3 cup raw cashews; 1 block extra-firm tofu, drained and pressed for 1 hour, torn into small pieces; 2 tablespoons cornstarch; Kosher salt; 1/4 cup soy sauce; 2 tablespoons chili crisp, plus more for serving; 2 tablespoons fresh ginger, grated on a rasp; 1 tablespoon dark brown sugar; 1 tablespoon black vinegar or balsamic vinegar; 2 garlic cloves, grated on a rasp; 1/2 teaspoon toasted sesame oil; 2 tablespoons vegetable oil; Butterhead, Bibb or Boston lettuce, leaves separated, to serve; 1 1/2 cups honey-roasted peanuts, ground in a food processor; Thinly sliced avocado, to serve; Lime wedges, to serve