Bring 6 quarts water to boil and add 2 tablespoons salt.
Using a meat mallet or cleaver blade, pat each lamb piece until it's 1/16-inch thick. Onto each lamb piece place one slice of Prosciutto and 1 piece of cheese. Mix rosemary, mint and 2 tablespoons parsley and divide among 8 pieces of lamb. Season with salt and pepper and roll like a burrito to form a little package. Tie each with 2 pieces of butcher twine.
In a heavy bottom pot, heat olive oil until smoking. Brown lamb pieces 4 at a time until golden brown all over and remove. Add onions and garlic and cook until softened and lightly browned. Add chilies, red wine and tomato sauce and bring to a boil. Lower heat to medium and place meat in pan with sauces, submerging the meat halfway. Simmer uncovered for 20 to 30 minutes, or until lamb is fork tender.
Put orecchiette into boiling water and cook until al dente, about 6 to 7 minutes, and drain.
Remove meat from sauce and toss orecchiette into sauce. Remove strings from meat. Pour orecchiette into a large serving bowl. Place meat on top, sprinkle with cheese and serve.