Soak the mushrooms in water to cover for 15 minutes. Saute the garlic in the butter in a large frying pan. Add the tarragon, parsley, broccoli and mushrooms. Saute for 10 minutes. Season to taste with salt and pepper. Add salt to the boiling water. Cook the fettucine in the salted boiling water until al dente. Drain. Transfer to a serving bowl. Add a large gob of butter. Add the broccoli mixture. Toss. Pass the cheese separately.