In jar with screw-top lid, combine the 1/4 cup oil, lemon peel and juice, the 1/2 teaspoon salt and the 1/4 teaspoon black pepper. Cover and shake well; set aside.
Clean and trim asparagus; coat lightly with the 2 tablespoons oil. Sprinkle with salt and pepper. Set aside. Meanwhile, clean arugula or spinach and remove excess stems; dry. Set aside.
For a charcoal grill, grill asparagus crosswise on the rack of an uncovered grill directly over medium coals for 4 to 6 minutes or until crisp-tender, turning spears occasionally. (For a gas grill, preheat grill. Reduce heat to medium. Place asparagus crosswise on grill rack over heat. Cover and grill as above.)
While asparagus is warm, toss with arugula and dressing (this will wilt the arugula). Divide among 4 dinner plates and top with Parmesan curls. Serve immediately. Makes 4 servings.
