1. Steam the asparagus, covered, on a rack set over 1 inch simmering water, until crisp-tender, about 5 minutes.
2. Melt the butter in a small saucepan; stir in the asparagus; set aside.
3. Meanwhile, cook the fettuccine in plenty of boiling salted water until al dente, or firm to the bite, 2 minutes for fresh and 5 to 7 minutes for dried; drain.
4. Toss the fettuccine with the asparagus, butter, mozzarella, and dill. Sprinkle with caviar and black pepper.