Press the tofu for at least 10 minutes to drain excess liquid—this ensures the tofu browns properly rather than steaming in the pan. Once drained, crumble it into a bowl using your hands or a fork until it resembles small pebbles.

Whisk the cornstarch, vegan oyster sauce, sesame oil, hoisin sauce, water, dark brown sugar, and dark soy sauce in a small bowl until the cornstarch is completely dissolved and the sauce is smooth.

Heat the sesame oil in a large skillet or wok over medium heat until the oil shimmers. Sauté the onion, garlic, and ginger until the onion is translucent and the mixture smells aromatic, about 2 minutes.

Add the diced mushrooms and carrots, then increase the heat to high. Pour in the wine and cook for 2 to 3 minutes, stirring constantly, until the liquid has evaporated and the carrots are just tender.

Add the crumbled tofu and the stir-fry sauce to the skillet. Reduce the heat to medium-high and cook for about 10 minutes, stirring every few minutes, until the moisture has evaporated and the tofu looks dry and lightly browned.

Stir the sweet hoisin sauce ingredients together in a small saucepan over medium heat if using. Simmer and stir for about 2 minutes until the sauce thickens and becomes glossy.

Spoon the hot tofu mixture into the cold lettuce cups and garnish with peanuts, scallions, and chiles. Serve immediately while the filling is hot and the lettuce is crisp.