Place two (1 large and 1 medium) cast-iron skillets or oven-safe heavy skillets in a cold oven; heat oven to 450 degrees F. In a medium bowl combine asparagus and 1/2 teaspoon olive oil; sprinkle with salt and pepper. Brush the remaining1 teaspoon of olive oil on both sides of fish; sprinkle lightly with salt and pepper.
Carefully remove hot skillets from oven. Place fish, skin side down, in the large skillet. Place asparagus in medium skillet. Return skillets to oven. Bake for 12 minutes, or until fish flakes easily when tested with a fork and asparagus is crisp-tender.
To serve, sprinkle fish with lemon peel and parsley.