Rinse the octopus thoroughly under cold water to remove debris and impurities. Pat it dry with a paper towel.

In a large pot, combine the water with halved onion, smashed garlic, bay leaves, peppercorns, vinegar or wine, salt, and optional vegetables. Bring to a gentle boil.

Once boiling, reduce heat to maintain a low simmer for about 5 minutes.

Carefully lower the cleaned octopus into the simmering broth to ensure even cooking.

Cover loosely and let simmer for 45 to 60 minutes, check for doneness by piercing the thickest part.

After cooking, let the octopus rest in the hot broth for an additional 10 minutes.

Transfer to a cutting board, slice into bite-sized pieces or leave whole, drizzle with olive oil and lemon juice.