Heat your oven to 300 degrees. Trim the stems off the brussels sprouts and remove any browned outer leaves. Slice the sprouts into halves or quarters, and place them in a medium bowl.

Melt the butter and pour it over the brussels sprouts. Add the garlic, parmesan, and a generous amount of salt and pepper. Stir to combine.

Pour the seasoned brussels sprouts onto a parchment-lined baking sheet and place them in the oven. Let bake for about 40 minutes, until they are just starting to brown.

Chop up the prosciutto, and stir it into the brussels sprouts. Increase the heat to 350 degrees and let the brussels sprouts roast for another 10-15 minutes until browned. Serve immediately.