In a large saucepan (soup pot) over high heat, bring conch and 8 cups water to a boil. Drain and set aside.
In a large skillet over medium high heat, melt shortening (or bacon fat). Stir in onion, celery, bell pepper, carrot and garlic and saute until browned. You may have to cook in batches depending on size of skillet. Transfer vegetable to soup pot when cooked.
Add drained conch and 3 quarts of water to soup pot along with potatoes, tomato puree, tomato paste, oregano, basil, bay leaves and hot pepper sauce.
Put soup pot over high heat and bring to a boil. Reduce heat and simmer for 1 1/2 hours or until conch are tender and potatoes are cooked. Discard bay leaves. Add salt and pepper to taste.