In a large pot, heat the oil. Add the garlic, celery, carrots, and onion and cook over moderate heat, stirring occasionally, until softened, 7 minutes. Add the tomatoes, bay leaf, lentils, smoked turkey, and 2 quarts of water and bring to a boil. Cover partially and simmer, stirring occasionally, until the lentils are very tender, 1 hour. Add the potatoes and simmer until tender, 10 minutes.

Remove the turkey meat from the bones and return it to the soup; discard the skin, bones, and bay leaf. Add the parsley and season the soup with salt and pepper. Ladle the soup into bowls and serve, passing the cheese at the table.

The lentil soup can be refrigerated for up to 3 days.