Heat the oil in a large pot over medium heat. Add the chopped onion, garlic, green bell pepper, and red bell pepper. Sauté until the vegetables are softened and fragrant.
Stir in the tomato paste, thyme, bay leaves, and allspice. Cook for a few minutes until the tomato paste is well incorporated.
Add the diced potato, carrot, and hot pepper to the pot. Pour in the vegetable or chicken broth. Bring to a boil, then reduce heat to low and simmer until the vegetables are tender, about 20-25 minutes.
Add the chopped callaloo to the pot and cook for an additional 10-15 minutes, or until the callaloo is wilted and tender.
Use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a blender and blend until smooth, then return to the pot.
Stir in the coconut milk and season with salt and black pepper to taste. Heat through, but do not let it boil.
Garnish with chopped fresh parsley before serving.
Enjoy your meal!