1. Rub the inside of a large salad bowl with cut sides of garlic clove; discard garlic.
2. Add oil, lemon juice, oregano, salt, and pepper to bowl; whisk well. Add artichokes, tossing gently; let stand at room temperature.
3. Meanwhile, place edamame in a large pot of boiling salted water; cook 2 minutes. Add asparagus; cook until asparagus and edamame are crisp-tender (about 3 minutes). Rinse under cold water, drain well, and blot dry with paper towels.
4. Add asparagus and edamame to artichoke mixture; toss. Transfer to 4 individual plates. Arrange shaved Parmesan over each salad. Serve.