Preheat oven to 400 degrees F. Toss brussel sprout halves in olive oil, then spread in a single layer on a baking sheet. Roast in preheated oven for 35-40 minutes, turning half way through cooking process.
Reduce heat to 375 degrees F.
Cut prosciutto slices into squares. Using two pieces where the top one is rotated slightly, press down into a mini muffin tin to create a cup or bowl shape. Bake in preheated oven for about 15 minutes or until crisp. Transfer to a paper towel to drain.
To serve, add a roasted brussel sprout half to each prosciutto cup.
If making ahead, roast brussel sprouts ahead of time but do not make prosciutto cups until ready to serve. During the last 5 minutes of cooking, add the brussel sprout half to the cup to warm it up. Serve warm.