Preheat the grill and brush any bits of crud and soot off with a grill brush. Run an oiled cloth over the grill grate after it has been brushed to pick up any of the loosened material.
Toss the asparagus with olive oil and salt, to taste. Put on the grill and sear on all sides until the asparagus is charred and crispy, about 6 to 7 minutes. Remove from the grill to a plate and reserve.
In a bowl toss, together the arugula, onion and Parmesan and dress with high quality extra-virgin olive oil and the Meyer lemon juice. Season with salt, to taste.
Arrange a few asparagus spears on 4 plates. Lay 2 prosciutto slices in a crinkly fashion on each portion. Top with the arugula salad and serve.