Snap off the tough bottoms of the asparagus and discard. Wash spears and pat dry, then place in a 9x13-inch baking dish.
Pour olive oil over asparagus and roll spears until evenly coated.
Arrange spears in a single layer and season with salt and freshly ground pepper to taste.
Cover dish with foil and bake 12 to 15 minutes until asparagus is tender when pierced with the tip of a knife (dish can be prepared ahead to this point).
Pass a vegetable peeler across the surface of room-temperature Parmigiano-Reggiano to create 1/4 cup of thin slivers. Scatter the slivers over the asparagus and return the dish to the oven. Continue baking just until cheese softens, about 2 to 3 minutes.
Place asparagus onto warm plates and sprinkle with several drops of balsamic vinegar and the chopped parsley or snipped chives.