Clean the conch meat thoroughly and tenderize it by pounding with a meat mallet or the side of a knife. Cut into bite-sized pieces.
Heat the vegetable oil in a large skillet or pot over medium heat. Add the chopped onion, garlic, and bell pepper. Cook until the vegetables are softened, about 5 minutes.
Stir in the chopped tomatoes, thyme, paprika, allspice, and cayenne pepper (if using). Cook for another 5 minutes.
Add the conch pieces to the skillet. Cook, stirring occasionally, until the conch is browned on all sides, about 5-7 minutes.
Pour in the vegetable or chicken broth and white wine (if using). Bring to a boil, then reduce the heat to low. Simmer, covered, for about 30-45 minutes, or until the conch is tender.
Stir in the lime or lemon juice and adjust seasoning with salt and black pepper to taste.
Garnish with chopped fresh parsley or cilantro before serving. Serve hot with rice, peas, or crusty bread.
Enjoy your meal!