In a small bowl, combine the tamari, lime juice, tamarind, and sugar. Mix well and set aside.
Cook the noodles in a large pot of boiling water until just al dente, about 3 minutes. Drain the noodles, toss with 1 tablespoon of the oil, and set aside.
Heat 1 tablespoon of oil in a large skillet over medium heat. Stir in the tofu, nutritional yeast, and turmeric. Cook, stirring, until the tofu is dry, 7 to 10 minutes. Transfer the tofu to a bowl, season to taste with salt, and set aside.
Heat the remaining 2 tablespoons oil in the same skillet over medium heat. Add the mushrooms and carrots and cook, stirring, until the mushrooms begin to brown, about 5 minutes. Stir in the garlic, chili paste, and bell pepper, and cook until the garlic is fragrant, about 30 seconds.
Add the noodles, spinach, bean sprouts, peanuts, reserved sauce, and reserved tofu. Cook, stirring, until the noodles are tender but not overcooked, the sauce has been absorbed, and everything is heated through. Serve hot garnished with cilantro and lime wedges.