4 appetizer servings.
3 tablespoons butter
Cook asparagus in large pot of boiling salted water until crisp-tender, about 3 minutes. Using slotted spoon, transfer to bowl. Add fettuccine to same pot and cook until tender but still firm to bite. Drain fettuccine. Return pasta and asparagus to same pot.
Meanwhile, melt butter in large skillet over low heat. Add garlic and tarragon and stir 1 minute. Add morels and sauté 4 minutes. Add cream and broth; boil until morels are tender and sauce thickens slightly, about 4 minutes. Stir in 1/2 cup Parmesan cheese.
Add sauce to pasta and asparagus; toss to coat. Season with salt and pepper. Pass remaining Parmesan separately.