Prep asparagus. Fill a large bowl with ice water and set it aside. Cut off the tough bottom portion of the asparagus spears -- this is usually about 3-inches or so. It should actually "snap" off at the right place if you use your hands. Then peel the asparagus and set up a steamer on the stove with water just beneath the rack. Bring the water in the steamer to a boil and place the peeled asparagus spears on the rack and cover. Steam until tender, about 6 minutes, depending on how thick the spears are. (They should not be soft, just tender.)Drain the asparagus and "shock" it by placing it in the bowl of ice-water for about 3 minutes. This will stop it from cooking any further and help to keep the bright color. Drain again and pat dry with paper towels. Cut the spears in half or into bite-sized pieces.
Combine salad ingredients. In a large mixing or serving bowl, toss the asparagus with the greens, onions and cheese. Set aside.
Make the dressing. In a small mixing bowl, combine the lime juice with the mustard, honey and salt. Gradually whisk in the olive oil and season to taste with the pepper and more salt if necessary. (You can also add all of the ingredients to a small jar and shake.)
Add dressing and serve. Toss the salad with the dressing and serve at once!