Rinse the octopus with cool water and lay it on a cutting board to inspect it make certain it’s clean and no ink sac is still attached. Cut off the root end of the onion and cut it in half. Place both into a large pot along with the bay leaves.
Fill the pot about ¾ full with water, put it on the stove over high heat, cover it with a lid, and bring it to a boil. Once it’s boiling, reduce the heat to medium and tilt the lid so steam can escape while it simmers. Allow it to cook 40-50 minutes.
On a clean cutting board, cut the cherry tomatoes in half, finely dice the bell peppers and red onion and set them aside in separate piles. Chop the parsley and oregano and set them aside. Have the capers and olives set aside with the rest of the vegetables and ready to use.
Using a fork, check the doneness of the octopus by inserting the fork into the onion. If it goes in easily, the octopus will be done and tender. Transfer the octopus to a clean cutting board and let it cool for 5-10 minutes. Discard the onion and bay leaves.
Cut the head off the octopus and check the center where the tentacles are attached for a hard beak like piece. If it’s there, remove it with your fingers and discard.
Cut the rest of the octopus into ½ inch size pieces. Leave the ends of the tentacles a little longer so they can curl up.
Put the cut tomatoes, peppers, onion, oregano, parsley, capers, olives, and octopus into a large bowl and stir well to combine.
Peel and mince the garlic cloves and cut the lemons in half. Pour the olive oil into a bowl, add the garlic, and squeeze the lemon juice into the bowl. Remove any seeds that may have dropped in, then season with the black pepper and salt, whisking well to combine. Taste and add more salt if needed.
Pour the dressing over the salad, stir again, and cover. Refrigerate for at least 30 minutes to 1 hour. Serve cold.