Method

1. Make the causa. Place the potatoes in a large saucepan and add enouth water to cover (about 5 liters). Add 10 ml. of salt and bring to a boil over medium-high heat. Reduce the heat to medium, cover partially and boil gently until tender, about 25 minutes. Drain and return to the pot. Cover tightly and let steam for 5 minutes.
2. Prepare the octopus while the potatoes cook. Bring 1.5 liters of water and 15 ml. of salt to a boil over high heat in a medium saucepan. Cut each octopus into two sections by slicing the tentacles off the body at the point where they are joined. Drop the tentacles into the boiling water and cook for 1 minute, then remove with a strainer and transfer to a bowl of ice water to stop th cooking; drain well when cool. Drop the head and body pieces into the boiling water and cook for 2 to 3 minutes, or until the interior of the thickest part of the bodies has just turned from translucent to completely opaque (you can slice them crosswise to check this). Transfer them to a bowl of ice water and drain well when cool. Dry the octopus with paper towels, then cut the heads and bodies into 3mm thick slices, leaving the tails whole.
3. Use a food mill or ricer to purée the potatoes into a large mixing bowl. Add the oil, lime juice, rocoto chili paste, piquillo purée, and 30 ml. of salt. Use a wooden spoon to stir until well blended. The purée should be very smooth.
4. Oil a 23 cm. springform pan and line the plastic. Lightly oil the plastic. Place 1 liter of the puréed potatoes into the mold. Arrange the tomato slices so they evenly cover the surface of the potato. Then layer the avocado slices over the tomato slices. Spoon the remaining potato mixture over the avocado slices completely covering them. Cover and chill in the refrigerator until cold, about 3 hours.
5. Make the olive sauce. Use a food processor to blend the mayonesa with the olives, processing it until almost smooth. Season with the pepper and add the lime juice. Refrigerate for at least 2 hours to allow the flavors to blend.
6. Unmold the causa onto a large plate. Top the causa with the sliced octopus and garnish with 30 ml. of the capers. To serve, slice into 8 wedges and top with about 75 ml. of sauce and some of the remaining capers.