Peel the yucca root and cut into 2-inch chunks, removing the fibrous core. Peel and dice the sweet potatoes into similar-sized pieces. Cut the bell peppers and chayote into 1-inch cubes. Dice the onions and mince the garlic and cilantro.

Heat olive oil in a large stockpot over medium heat. Add the diced onions and cook for 5 minutes until softened and translucent. Add the minced garlic and cook for another minute until fragrant.

Add the cubed bell peppers to the pot and sauté for 3-4 minutes. Stir in the cumin, oregano, paprika, and black pepper. Cook the spices for 1 minute to release their aromas.

Add the diced tomatoes with their juices, tomato paste, and 6 cups of water or vegetable broth. Stir well to combine all ingredients. Bring the mixture to a boil over high heat.

Once boiling, add the yucca chunks, sweet potato pieces, and black beans. Reduce heat to medium-low and simmer uncovered for 25 minutes, stirring occasionally.

Add the chayote cubes to the pot and continue simmering for another 15-20 minutes until all vegetables are fork-tender but not mushy. The yucca should be soft and creamy.

Stir in the fresh cilantro and lime juice. Taste and adjust seasoning with salt as needed. Let the guiso rest for 5 minutes before serving.

Ladle the hot stew into bowls and serve immediately with extra cilantro and lime wedges on the side.