Preheat the oven to 400 F. Line a baking sheet with parchment paper.

Drain the water from the tofu and wrap it in a kitchen towel or paper towel. Place the wrapped tofu on plate with something heavy - like a pan - on top. Let tofu sit for at least 15 minutes to drain the water.

Prepare the sauce. In a bowl, add the hoisin sauce, soy sauce, rice vinegar, and 2 tablespoons of olive oil. Whisk well to combine.

Cut the tofu in half vertically and then cut into small cubes. Sprinkle the cornstarch over the tofu and gently toss, so that all of the tofu is coated with the cornstarch.

Add the cubed tofu to the bowl with the sauce and gently toss the tofu until it’s all fully covered.

Set aside and let the tofu marinate in the sauce for about 15 minutes.

While the tofu is marinating, prepare the vegetables. Add the remaining 3 tablespoons of olive oil to a pan over medium heat. Add the carrots, mushrooms, and water chestnuts and sauté for about 5 minutes, stirring occasionally, until soft.

Remove the tofu from the sauce, reserving the extra sauce, and place it in a single layer on the baking sheet. Bake in the preheated oven for 20 minutes, gently tossing the tofu halfway through.

Pour the remaining sauce over the vegetables and turn the heat down to low. Cook for another few minutes, stirring occasionally, until the sauce thickens considerably.

Assemble the lettuce wraps. You’ll have about 7-8 wraps - I recommend using 2 lettuce leaves for each “wrap.” Top each one with a heaping spoonful of tofu, followed by about a tablespoon of the vegetable mixture.

Garnish with sesame seeds and green onion.