Fill a large saucepan with enough water to generously cover the octopus. Bring to the boil over high heat.
Plunge the octopus in the boiling water for 15 seconds, then use tongs to carefully remove and transfer to a large bowl. Once again bring water to the boil, then repeat the process of plunging the octopus tentacles and removing another four times, allowing the water to boil each time before plunging the octopus. After the forth immersion, reduce the heat to low. Allow the octopus to cook, testing from time to time, until tender (approximately 30-40 minutes).
Note: Nonna’s octopus salad can be prepared up to 1 day ahead. If preparing 1 day or hours ahead, complete steps 1-2 then refrigerate, covered with cling film (plastic wrap).
Drain the octopus in a colander. Allow to cool completely, then transfer to a chopping board. Roughly chop the octopus and transfer to a mixing bowl. Add the celery, carrot, lemon juice, garlic clove, mint, parsley, and extra virgin olive oil. Season with sea salt to taste and stir to combine. Set aside for 30 minutes for the flavours to develop.
Discard garlic clove. Transfer to a serving dish and serve – buon appetito.