Thaw frozen octopus overnight in the fridge. Bring a large pot of water to a gentle boil and add the bay leaves and peppercorns. Do not add salt.
Lower the octopus into the pot, reduce to a bare simmer, and cook for 45 to 60 minutes, until a knife slides through the thickest part of a tentacle with almost no resistance.
Remove the octopus and let it cool just enough to handle. For optional smoky char, brush with oil and sear on a hot grill or pan for about 1 minute per side.
Make the Salad
Cut the tentacles into 1-inch pieces and add them to a large bowl. Discard the head or reserve for another use.
Whisk together the olive oil, lemon juice, red wine vinegar, minced garlic, and oregano.
Pour the dressing over the warm octopus and toss gently so it absorbs the lemon and oil.
Fold in the red onion, Kalamata olives, capers, cherry tomatoes, and parsley.
Season with salt and pepper, then taste and adjust. Let rest 20 to 30 minutes, finish with more oregano, and serve at room temperature.
Notes
Dress it warm: Warm octopus soaks up the ladolemono dressing far better than cold, which is the secret to taverna flavor.
Go easy on the salt: The olives, capers, and octopus are already briny, so season lightly and taste before adding more.
Frozen is best: The freeze-and-thaw tenderizes the octopus, so frozen gives more reliable results than fresh.
Make ahead: Keeps 2 to 3 days refrigerated and tastes even better the next day. Bring to room temperature before serving.