Preheat the oven to 400°F (204°C).
Sprinkle the fillets with salt and pepper. Place a sprig of rosemary on each of the fillets, then wrap them individually in a prosciutto slice.
Grease a 6 x 10 inch (15 x 25 cm) baking dish with some of the butter, then carefully place the wrapped fillets in the dish. Bake until the fish is white and flaky, about 15 to 20 minutes.
While the fish cooks, melt the remaining butter in a small saucepan with the remaining sprig of rosemary on very low flame, until the butter begins to brown, about 2 minutes.
Serve the fish immediately, drizzled with some of the rosemary butter.