Lentil Sausage Soup

INGREDIENTS

• 6 carrots, unpeeled and halved
• 1/4 cup olive oil, plus extra for serving
• 1 head garlic, unpeeled and cut in 1/2 crosswise
• 1 pound French green lentils (recommended: du Puy)
• 3 large onions, unpeeled and quartered
• 2 tablespoons kosher salt
• 3 quarts Homemade Chicken Stock, recipe follows, or canned broth
• 4 celery stalks with leaves, cut in thirds
• 1 tablespoon minced fresh thyme leaves
• 4 parsnips, unpeeled and cut in 1/2, optional
• 3 cups medium diced celery (8 stalks)
• 3 (5-pound) chickens
• 20 sprigs fresh dill
• 2 teaspoons whole black peppercorns
• 4 cups chopped leeks, white and light green parts only (2 leeks)
• 1 teaspoon ground cumin
• 1 1/2 teaspoons freshly ground black pepper
• 1 pound kielbasa, cut in 1/2 lengthwise and sliced 1/3-inch thick
• 1 tablespoon minced garlic (2 large cloves)
• Freshly grated Parmesan, for serving
• 2 tablespoons dry red wine or red wine vinegar
• 4 cups diced yellow onions (3 large)
• 15 sprigs fresh thyme
• 3 cups medium diced carrots (4 to 6 carrots)
• 1/4 cup tomato paste
• 1 tablespoon kosher salt
• 20 sprigs fresh flat-leaf parsley