Break off the ends (the bottom 1″ or so) of the asparagus. With a vegetable peeler, beginning just before the tips, shave the asparagus to where it is paper thin but not so thin that you cannot shave a full strip. Reserve the tips and slice them thinly with a knife. Add the asparagus to a bowl and dress like a salad with the lemon vinaigrette (note: it may not require all of it). Add the grated Pecorino Romano. Season to taste with salt and pepper. Add the asparagus to plates and shave the remaining Pecorino Romano with a vegetable peeler. Garnish the asparagus with the shaved Pecorino Romano.