Cook the Octopus: Add the shallot, bay leaves, parsley, garlic, peppercorns, white wine, salt, and water to a medium pot. Bring to a gentle simmer.
Add the octopus tentacles and keep the liquid at a steady simmer (not boiling). Cook for 40 minutes to 1 hour, checking every 10 minutes after the 40-minute mark.
To test for doneness, insert a paring knife into the thickest part of the tentacle. If it slides in easily, it’s ready. If it bounces back or resists, continue cooking another 10–15 minutes and check again.
Clean the Octopus: Once tender, remove the octopus and let it cool until safe to handle.
If there is any slimy outer membrane, gently scrape or peel it off using a paring knife or spoon. Rinse briefly under cold water if needed and pat dry. Slice the octopus into ½-inch pieces.
Make the Salad: In a large bowl, combine the chopped octopus, shaved fennel and onion, pickled peppers, olives, parsley, and oregano.
Make the Vinaigrette: Whisk together the olive oil, lemon juice, grated garlic, salt, and pepper.
Assemble: Pour the vinaigrette over the salad and toss gently to combine. Taste and adjust seasoning as needed.
Chill: Let the salad marinate for at least 20 minutes before serving. Longer is even better.