Octopus, Fennel and Potato Salad with Aïoli

To tenderize an octopus, some people suggest throwing it hard into the sink about ten times; others, banging it with a mallet; and others use the timeless method of hanging it on a rope by the sea, to dry in the wind and sun for a day or so and then beating it against a nearby rock. One recipe recommends putting the cleaned octopus in a dry, covered pan over a medium heat for 15 minutes, before adding any liquid. Another, much the best, simply leaves it in the freezer for a few hours and th