Rinse the asparagus under cold running water. Dry, snap off the woody ends (they will break naturally at the right point). Lightly sprinkle with sea salt and pepper, wrap in slices of Parma ham, brush with a tablespoon of extra virgin olive oil, place on a plate. Pour the asparagus with soy sauce, rice vinegar, lemon juice, remaining extra virgin olive oil, and honey, soak in the resulting sauce, and set aside.
Rinse the beet greens and dry, cut off the tough stems. Place the leaves in a salad bowl. Rinse the radishes and slice (with a knife or vegetable peeler into very thin strips). Place in the salad bowl with the beet greens.
Place the asparagus on a heated grill, reserve the sauce. Grill until the ham is lightly browned and the asparagus is tender (but should remain crispy). Cut into smaller pieces, add to the salad bowl with the beet greens and radishes, pour the reserved sauce over. Sprinkle with Parmesan. Season if needed.