Cook pasta according to package directions. Drain; keep warm.
Meanwhile, in a large skillet cook garlic in hot oil over medium-high heat for 30 seconds. Add green tomatoes; cook for 3 to 4 minutes or until heated through, stirring often. Stir whipping cream, parsley, and pepper into tomato mixture. Cook over medium heat for 5 to 8 minutes or until slightly thickened, stirring occasionally. Remove from heat.
Stir the 1/3 cup Parmesan cheese and the prosciutto into sauce. Serve sauce over orecchiette. Top with additional Parmesan cheese, if desired. Makes 4 main-dish servings.