Rinse the octopus well under cold water and clean the sac, making sure to get rid of any grit. Flip the octopus over and look for the beak (the dark, hard, crusty shell-like bit) and scoop out with a paring knife. Add the beak and octopus to a large pot and cover with water. Bring to a boil, and then lower to medium-high heat and cook until the octopus is fork tender, about 40 minutes. Drain and let cool, and then cut into bite-size pieces. Meanwhile, peel your potatoes, cut into bite-size pieces and cover with cold water in another pot. Bring to a boil and cook until tender. Combine the octopus, potatoes, olive oil and lemon juice and season with salt and pepper. Add the black olives and parsley to finish.
Recipe courtesy of David Rocco