1 tablespoon extra-virgin olive oil
3 garlic cloves, peeled
2 celery ribs, finely chopped
2 carrots, finely chopped
1 onion, finely chopped
One 16-ounce can whole tomatoes, chopped and juices reserved
1 bay leaf
1 cup green or brown lentils
3/4 pound smoked turkey wing and thigh
4 small red potatoes, peeled and sliced 1/4 inch thick
1/4 cup chopped flat-leaf parsley
Salt and freshly ground pepper
Freshly grated Parmigiano-Reggiano cheese, for serving