Bring 6 quarts of water to a boil and add 2 tablespoons salt. Add the potatoes and cook until tender but not falling apart. Drain and allow to cool for 10 minutes, then peel and slice potatoes into 1/2-inch thick slices.
In a hot rondeau heat 1/4 cup olive oil, add octopus, red pepper flakes, and garlic. Cook over high heat for about 40 minutes or until octopus is tender and has released its juices. Season octopus with salt and pepper. Allow to cool and then slice into 1/2-inch pieces.
Mound the octopus slices attractively in the center of a platter and arrange the warm potato slices around the edge. Sprinkle with the scallions and parsley. Mix together the olive oil, lemon juice, garlic, red onion, salt, and pepper.
Taste and adjust the seasoning, then pour the dressing over the octopus and still warm potatoes. Cover with a piece of foil and set aside in a cool place to marinate for several hours before serving.