Wash the octopus clean and cut apart the tentacles if necessary.
Twist the tentacles and wrap them tightly as a roll with cling film.
Wrap tightly in foil, twisting the ends of the foil to seal. Place in a large pan of cold water and slowly bring to the boil. Simmer for 60-70 minutes over a low heat. Allow to cool completely.
Blanch the broad beans in boiling salted water for 5-6 minutes. Rinse under ice cold water, drain then squeeze between your thumb and index finger until the hard skin cracks and releases the bean inside. Discard the skins.
Wash the basil, shake dry and pick off the leaves. Mix with the beans in a blender to a smooth paste.
Season the bean paste with lemon juice, salt and pepper. Stir in the olive oil.
Unwrap the octopus. Cut the roll into slices and arrange on plates. Pour the bean puree on top, garnish with broad beans and basil. Serve with lemon wedges.