Place the tongue, carrots, onion, celery, leek, garlic, and bay leaves into stock pot. Add water until all ingredients are submerged. Bring to a boil, reduce to a simmer, and cook for 8 hours with the lid on but tilted.
Pull the tongue out of liquid and peel the outer layer of skin off. Chop the tongue meat into cubes.
Heat the butter in a sauté pan over medium-high heat. Add the tongue, cayenne, lime, salt, and pepper to taste. Cook until tongue is browned all over.