Heat the vegetable oil in a large pot over medium heat. Add the chopped onion, garlic, and bell pepper. Cook until the vegetables are softened, about 5 minutes.
Add the diced potato and carrot to the pot. Cook for an additional 5 minutes, stirring occasionally.
Pour in the vegetable or chicken broth. Add the thyme, allspice, paprika, salt, and black pepper. If using, add the hot peppers for extra heat. Bring the mixture to a boil, then reduce the heat and let it simmer until the potatoes and carrots are tender, about 15 minutes.
Stir in the chopped callaloo leaves (or spinach/kale). Cook for an additional 5-7 minutes, until the greens are wilted and tender.
Use an immersion blender to blend the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and blend until smooth.
Return the blended soup to the pot. Stir in the coconut milk and cook for a few more minutes until heated through. If using, add the diced ham or bacon and fresh parsley. Adjust seasoning to taste.
Ladle the soup into bowls and serve hot.
Enjoy your meal!