1. In dry wok, cook pine nuts over low heat, stirring often, until lightly toasted, 2 to 3 minutes. Transfer to plate and set aside.
2. In same wok, bring 2 1/2 quarts lightly salted water to a boil over high heat. Add pasta; stir to prevent sticking. Cook, stirring occasionally, until just tender, 10 to 12 minutes. Drain well and set aside. Dry wok.
3. Set wok over high heat and add 1 1/2 tablespoons oil. Add mushrooms and 1 teaspoon salt and stir-fry until tender, about 2 minutes. Transfer to medium bowl and set aside.
4. Return wok to high heat and add remaining 1 tablespoon oil. Add garlic and onion and stir-fry 1 1/2 minutes. Add remaining 1/2 teaspoon salt, rosemary and pepper flakes and stir-fry 1 1/2 minutes. Add broth and bring to a boil. Reduce heat to low and simmer 2 minutes, scraping up brown bits from bottom of wok. Add to bowl with mushrooms.
5. Return wok to high heat. Add mirin and mustard and stir with wire whisk to blend. Bring to a simmer then add reserved pasta and mushroom mixture and cook, stirring, 2 minutes. Toss in toasted pine nuts and serve.