Preheat oven to 400º. Place asparagus in a large baking dish and sprinkle with olive oil. Arrange in a single layer and roll to evenly coat. Season with salt and pepper.
Cover with foil and bake for 12-15 minutes until asparagus is tender when pierced with a knife. Remove from oven.
With a vegetable peeler, shave Parmigiano-Reggiano into slivers. Scatter the cheese over the asparagus and return the dish to the oven. Continue baking just until the cheese softens, about 2-3 minutes.
Place the asparagus on warmed plates and drizzle with balsamic vinegar. Serve.