Rioja Braised Lamb Shanks with Chorizo and Garlic

Name: Rioja Braised Lamb Shanks with Chorizo and Garlic
Ingredients: 2 tablespoons vegetable oil; 4 lamb shanks; Kosher salt; Freshly ground black pepper; 1 1/2 cups Rioja or 1 1/2 cups good quality beef stock; 1 cup good quality balsamic vinegar; 1 bulb garlic, cut in half horizontally; 2 bay leaves; 1 teaspoon paprika, or to taste; 1/2 teaspoon whole black peppercorns; 4 sprigs fresh rosemary; 1 1/4 cups good quality beef stock; One 4-ounce piece chorizo; 1 large red onion, cut into wedges; 2 carrots, chopped; 1 tablespoon honey