Place the rice noodles in a large heatproof bowl. Cover with boiling water and let soak for 30 minutes, or until tender. Drain and set aside.
Pat the tofu dry with paper towels and cut into 1-inch cubes. Toss gently with the cornstarch.
Heat a wok or large nonstick skillet over medium-high heat. Add 2 tablespoons/30 milliliters oil and cook the tofu for 6 to 8 minutes, turning occasionally, until golden and crisp on all sides. Transfer to a plate and set aside.
Lower the heat to medium. Add a splash of oil if needed, then sauté the garlic, ginger, and chopped lemongrass for about 1 minute, until fragrant. Add the mushrooms and cook for 3 to 4 minutes, until softened. Push the vegetables to one side of the pan. Crack in the egg and scramble until just set. Stir to combine.
In a small bowl, whisk together the light soy sauce, dark soy sauce, brown sugar, fish sauce (if using), and boiling water. Pour the sauce into the pan and bring to a simmer.
Add the drained noodles, tofu, bean sprouts, scallions, and cabbage or carrots (if using). Toss everything together until well coated and heated through, about 2 to 3 minutes.
Serve hot, topped with roasted peanuts, fresh cilantro, and lime wedges. Offer extra bean sprouts and crushed peanuts at the table.