Peel the carrots and celery and cut into ½-inch dice. Peel the onion and cut into 1-inch chunks.
Lightly crush and peel the garlic cloves and put them in a heavy-bottomed braising pan with the olive oil. Place over medium-high heat. When the garlic is lightly browned on all sides, remove and discard it. Add the lamb shanks to the oil and brown them on all sides