Prepare the grill for cooking over medium heat (400°F).
In a small bowl whisk the mayonnaise ingredients.
Remove and discard the tough bottom of each asparagus spear by grasping each end and bending it gently until it snaps at its natural point of tenderness, usually two-thirds of the way down the spear. For very thick spears, after snapping off the thick ends, use a vegetable peeler to peel off the outer skin from the bottom half of each spear.
Related Grill Skills
Spread the asparagus on a large plate. Drizzle the oil over the top and season evenly with the salt and pepper. Turn the spears until they are evenly coated.
Brush the cooking grates clean. Grill the asparagus (perpendicular to the grate) over medium heat, with the lid closed, until browned in spots but not charred, 6 to 8 minutes, turning occasionally. Remove from the grill and keep warm.
Grill the prosciutto slices over medium heat just until crisp, 2 to 3 minutes, turning once. Remove from the grill and cut each slice into pieces about 2 inches across.
Arrange the prosciutto and asparagus on four plates and spoon the mayonnaise over the top. Serve immediately.