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In a stockpot, warm the olive oil over medium heat, then add the onion. Sauté until translucent and softened, about 4 minutes. Add the garlic, allspice and thyme and sauté until aromatic, about 1 minute.
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Add the green onions, bay leaves, coconut milk and water. Bring to a simmer, then add the pumpkin and taro and cook for 5 minutes. Reduce heat if it turns into a boil. Add the potatoes and cook for another 3 minutes. Stir in the okra, plantain and carrots and cook for another 5 minutes. Finally, remove the green onions (and any bay leaves and thyme sprigs), then add the collard greens; simmer until darkened and bright green, about 4 more minutes. At this point, all of the vegetables should be easily pierced with a fork.
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Remove from heat and add the lime juice. Add salt and pepper to taste; stir in the cilantro and serve.
Notes
To give the stew more spice, add a Scotch bonnet or habanero pepper when adding the coconut milk and water and remove before serving. For more spice, burst the pepper in the stew before removing it.