How to Make It
In a large enameled cast-iron casserole, heat 2 tablespoons of the olive oil. Add the octopus and cook over moderately high heat, turning, until lightly browned all over, 2 to 3 minutes. Transfer the octopus to a plate. Add the garlic cloves to the casserole and cook over moderate heat, stirring, until lightly browned, about 2 minutes. Add the crushed red pepper and cook, stirring, until fragrant, about 20 seconds. Carefully add the white wine and bring to a boil. Return the octopus to the casserole; if necessary, add up to 1 cup of water to cover the octopus. Cover the casserole and braise over moderately low heat until very tender, about 1 hour and 30 minutes. Transfer the octopus to a plate and let cool completely.
Meanwhile, in a large bowl, whisk the red wine vinegar with the lemon juice, oregano and 2 tablespoons of the olive oil. Add the fennel, carrot, onion, scallions, chickpeas and a generous pinch of salt and mix well. Let stand for 30 minutes or up to 4 hours, stirring occasionally. Stir in the parsley and season the salad with salt.
Using a paper towel, wipe the purple skin off the octopus tentacles, leaving the suckers intact. Cut the tentacles in half lengthwise, then cut them into 3-inch lengths. Cut the head into 1 1/2-inch pieces.
In a large skillet, heat the remaining 2 tablespoons of olive oil. Add the octopus cut side down and cook over moderately high heat until well-browned on the bottom, about 1 minute. Turn the octopus and cook for 20 seconds longer. Transfer the seared octopus to a paper towel—lined plate to blot any excess oil and season lightly with salt. Transfer the octopus to plates. Fill the radicchio leaves with the Italian salad and set beside the octopus. Garnish with fennel fronds and serve.