Place the halved mozzarella sticks on a wax-paper-lined platter or tray and freeze, at least four hours and preferably overnight.
Preheat your oven to 400 degrees F. Line a rimmed broiler-safe baking sheet with unbleached broiler-safe parchment paper or with nonstick foil.
Wrap each frozen mozzarella stick with a slice of prosciutto. Prosciutto is sliced very thinly, so a few pieces might tear when you try to remove them from the package. Don't worry about it - the torn pieces are the chef's bonus. :)
Place the wrapped mozzarella sticks, seam side down, on the prepared baking sheet. Bake for 2 minutes.
Switch the oven to broil, place the baking sheet on the top oven rack, directly under the broiler, and broil until prosciutto is crisp and mozzarella just starts to melt, about 1 minute. Serve immediately.