Place plantains, lime juice, stock and garlic in a large saucepan over medium-high heat and bring to a boil. Turn heat down and simmer until plantains are very soft, about 30 mins. Use a slotted spoon to transfer plantains and garlic to a food processor or blender and blend, gradually adding broth to make a paste. Pour paste back into saucepan and whisk over low heat until soup is thickened and heated through. Season with cayenne pepper, salt and pepper as desired.