Heat the oven to 450 degrees. Combine the bread crumbs and Parmesan.
Rinse asparagus and break off woody bottoms. Peel if thick. Lay stalks in a baking dish that will hold them in two or three layers. If the asparagus are thick, add a splash of water. Drizzle with the olive oil, sprinkle with salt and pepper; place in oven.
Roast until the asparagus are tender, 10 to 12 minutes. Test for doneness by piercing a spear with point of a sharp knife; it should slide in but meet a little resistance. (Up to this point, the recipe can be made as much as two hours before serving; just leave asparagus at room temperature.).
Turn on broiler and place rack as close as possible to heating element. Top asparagus with cheese-crumb mixture and run under broiler to brown for 1-2 minutes. Serve hot or at room temperature.