In a large pot of boiling water, add the soba noodles, stirring to separate. Return the water to a boil, then lower the heat and simmer until the noodles are fully cooked, about 8 minutes. Drain, then plunge into an ice water bath, using your fingers to separate the noodles. Transfer to a colander and rinse with plenty of cold water until the water runs clear; drain well.
In a large skillet, drizzle in 1 1/2 tbsp. sesame oil over medium-high heat. Add the mushrooms and season with salt and pepper. Cook, stirring, until lightly browned, 3 to 4 minutes. Transfer to a bowl.
Add the cabbage, carrots, scallions, lime zest and drained noodles to the mushrooms and toss well.
In a small bowl, whisk the remaining 1 1/2 tbsp. sesame oil with the lime juice, soy sauce and fish sauce. Drizzle over the noodles; toss gently.