Preheat the oven to 350°. In a baking dish, mix the mirin, vinegar and soy sauce. Add the tofu; let stand for 15 minutes, turning halfway through. Pour the marinade into a bowl. Bake the tofu for 10 minutes. Cut into 1/2-inch pieces.
Meanwhile, bring a large pot of salted water to a boil and fill a large bowl with ice water. Add the noodles to the pot and cook until al dente, 6 minutes. Drain the noodles, reserving 1/3 cup of cooking water. Immediately plunge the noodles into the ice water to cool; drain well. Transfer the noodles to a large bowl and add the bean sprouts and cilantro.
In a food processor, combine the peanut butter with 1 teaspoon of chili-garlic sauce. With the machine on, slowly add the 1/3 cup of reserved noodle cooking water. Pour in the reserved marinade, season with salt and process until combined. Pour the peanut sauce over the noodles and toss well. Transfer the noodles to bowls, top with the tofu and serve with lime wedges, peanuts and chili-garlic sauce.