Cut the head off the octopus. Combine the tentacles, parsley, olive oil, oregano, thyme, shallots and garlic in a cast-iron pot over medium-high heat. Cover and gradually bring the mixture to a boil. You don't need to add any liquid to the pot because the octopus will release its own braising liquid. Once it comes to a boil, reduce the heat to medium-low and simmer for 1 hour.
Remove the octopus from the heat and let cool in the braising liquid. On a large piece of plastic wrap, lay the tentacles top to tail. Season with salt and cracked pepper. Tightly roll up (it should look like a long sausage). Use more plastic wrap to secure the octopus, if necessary. Refrigerate for at least 4 hours (or overnight) to set.
For the potato salad:
Combine the gherkins, capers, oil, mustard, vinegar, potatoes, shallots, chiles, chives and parsley in a large bowl. Season with salt and pepper.
To serve, unwrap the octopus and thinly slice. Divide the octopus among plates, drizzle with olive oil and garnish with lemon zest and celery leaves. Serve the potato salad alongside.
The octopus head can be reserved and then sliced and eaten with the rest of the dish.