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 three times, allowing the water to boil each time before plunging the octopus. After the third immersion, add the potatoes and reduce the heat to low to allow the octopus and potatoes to cook, testing from time to time, until the octopus is tender (approximately 30-40 minutes).
Note: Octopus and potato salad can be prepared up to 1 day ahead. If preparing one 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 cut the octopus with kitchen scissors and transfer to a mixing bowl. Slice the potatoes in 1cm thick rounds and add to the mixing bowl. Add the lemon juice, extra virgin olive oil, chopped parsley and sprinkle with paprika. Season with sea salt to taste and toss to combine.
Transfer to a serving dish. Serve immediately or for best results, set aside for 30 minutes for the flavours to develop – buon appetito!