1. Place eggs in a medium saucepan with enough cold water to cover. Cover and bring to a boil over high heat. Uncover, reduce heat to low and simmer 10 minutes. Using a slotted spoon, place eggs in a large bowl of cold water. Gently crack eggs and leave in cold water 1 minute, then peel.
2. Return water to a boil over high heat. Add asparagus and 1/2 teaspoon salt. Cook until asparagus is crisp-tender, about 2 minutes. Drain.
3. In a medium bowl, whisk together oil, vinegar, Parmesan, parsley, lemon zest, pepper and remaining 3/4 teaspoon salt. Chop eggs and add to dressing. Stir in chickpeas, radishes, onion and asparagus. Divide salad among four plates lined with Bibb lettuce.