Parboil the whole Brussels Sprouts. (Add the Brussels Sprouts to salted, boiling water and cook until partially done - nearly fork tender - about 8 minutes.)
Preheat oven to 450ºF.
Drain Brussels Sprouts and place on a towel to mostly dry.
Transfer them to a large cast iron skillet.
Smash them with the bottom of a lightly oiled glass to about ¼" thick.
Drizzle with olive oil then sprinkle about ½ tsp. Parmesan on each one.
Roast until the edges are slightly browned and beginning to crisp, 12 to 15 minutes.