Beef Brasato with Pappardelle and Mint

trimmed boneless beef shank, cut into 2-inch pieces

bottle dry red wine

mint sprigs, stems reserved

Salt and freshly ground pepper

extra-virgin olive oil

peeled Italian tomatoes, crushed

fresh pappardelle

large garlic cloves, thinly sliced

Freshly grated Parmigiano-Reggiano cheese, for serving