Combine water and porcini in med. bowl. Let stand until porcini soften, about 40 mins. Drain; reserve soaking liquid. Chop porcini coarsely. Heat oil in heavy lg. skillet over med-high heat. Add fresh mushrooms and garlic and saute until brown, about 6 mins. Add porcini and saute until fragrant, about 4 mins. Add butter and thyme; stir 1 min. Add broth and 1.1/4 cups reserved mushroom soaking liquid. Boil until sauce thickens slightly, about 5 mins. Mix in 4 tbsp cheese. (Can be prepared 1 hour ahead). Let stand at room temp.
Cook pasta in large pot of boiling salted water until just tender but still firm to bite. Bring sauce to simmer over med-high heat. Drain pasta. Add to sauce; toss. Season with salt and pepper. Transfer pasta to bowl. Top with 4 tbsp cheese.