First cook. Preheat the oven to 500°F
If your octopus hasn’t already been cleaned by the fishmonger, here’s how to prepare it for cooking.
Rinse it under cold running water. Gently rub away any grit or sand. Place it on a clean cutting board.
Turn the head inside out, just as you would with a small bag. Use your fingers to remove everything inside the head, being careful not to rupture the ink sac. The ink sac looks like a small silvery or dark pouch.
Rinse the inside of the head thoroughly and turn it right side out.
Lay the head flat on the cutting board. Use a sharp knife to cut out the eyes. Discard the eyes and separate the head from the tentacles.
Flip the octopus, and you will see a firm, round opening. This is where the beak is located. Use your fingers to push the beak upward from the underside. It will pop out like a small hard kernel. Discard the beak and make a cut between any 2 tentacles so that it opens like a curtain.
OPTIONAL STEP: If you like the look of the curly tentacles, bring a pot of water to a boil and dip the very ends of the tentacles into the water for 5 seconds, remove, and repeat 2 or 3 times. This will coax them into those iconic curls that make grilled octopus look instantly impressive.
Place the octopus and its head in a large, deep baking dish. The octopus should fit snugly. Add the bay leaves, onions, peppercorns, vinegar, and white wine. Cover tightly with a heavy fitted lid OR with heavy-duty aluminum foil.
Cook in the oven for 60 minutes, then carefully remove the octopus from the pot and place it on a baking tray. Try not to touch the skin. The goal is to keep the skin intact so that it crisps on the grill. Refrigerate the octopus overnight or for at least 3 hours.
Make the gremolata. Add all of the gremolata ingredients to a bowl and mix well. Cover and refrigerate.
Make the squid ink mayo. Add the squid ink and mayo to a small bowl.
Second Cook. Remove the octopus from the refrigerator and gently coat in olive oil. Preheat the grill to high. Grill the octopus until slightly charred on both sides, approximately 2 to 3 minutes on each side.
Time to plate. Spread the squid ink mayo onto your serving tray. Lay the grilled tentacles on top and then cover them in the gremolata.
Serve warm or cold!