Pat the hen dry and season with salt. To a large pot, add the hen, recao, peppers, garlic, onion, annatto, coriander, oregano and season with salt. Add water to cover and bring to a boil.
Reduce the heat to medium-low and cook for 3-4 hours, until the meat falls off the bone. Remove the hen and strain the soup; discard the solids. Shred the meat and add it back to the soup. Season to taste with salt and keep warm.
Add 2½cm (1in) of olive oil to a large skillet and heat to 160C/320F. Peel the plantains and slice into 2½cm (1in) rounds. Add to the oil and fry for 4 minutes, until easily pierced with a knife. Remove from the oil and drain on kitchen paper. Keep the oil over a very low heat while you form the mofongo balls.
In a mortar, crush the garlic cloves and a pinch of salt with a pestle until it forms a paste. Add the plantains and mash until well combined. Add more salt to taste. Form the plantain mash into golf ball-sized rounds.
Bring the oil back up to 160C/320F. Add the mofongo balls to the hot oil and fry for 2 minutes, turning after the first minute, until they are a deep gold colour. Drain on kitchen paper.
Ladle the soup into bowls. Add the mofongo balls and garnish with sliced avocado and chayote.
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