To tenderize the fresh or frozen octopus, place it into a pot and cover with water. You can then season the cooking water with salt, pepper, garlic, bay leaf, pickling spice, etc. if desired. Bring water to a boil and cook for 40 to 60 minutes until tender. NOTE: If using pre-cooked octopus, go directly to the next step.
Remove the octopus from the hot water, rinse, and then place into a bowl. Drizzle with the olive oil and mix in the chopped garlic. Let the octopus rest and marinate at room temperature for 30 to 60 minutes.
Make the lemon herb oil by combining the olive oil, lemon juice, oregano, garlic, parsley, and salt & pepper. Next make the chili herb oil by combining the olive oil, chili paste, oregano, sand salt & pepper. Both sauces can be held at room temperature for up to 4 hours. Refrigerate if storing longer and then return to room temperature before using.
Preheat your cleaned and oiled grill to medium-high heat. You want the grill to be heated thoroughly so that the direct high heat sears and crisps the octopus without the risk of drying out the interior.
When ready to grill, place the octopus on the grill and sear until browned and crisped on one side, about 4 minutes. Carefully flip the octopus and brown the other side for about 4 minutes longer. Grilling time will vary depending on the heat of your grill and the distance of the octopus from the heat source.
Remove the grilled octopus and cut them into smaller pieces if desired, or just transfer them as is to a serving platter or plates.
Stir the two sauces to mix, then spoon over the octopus or serve on the side. Serve with the lemon wedges and optional leafy greens which can be lightly dressed with some olive oil and salt if desired.
NOTE: The octopus can be cooked and refrigerated up to three days in advance before grilling if desired. Be sure to cool, drain, and dry well before wrapping in plastic wrap and storing in the refrigerator. You can use either fresh or frozen octopus. If using fresh octopus, you will need to make sure it is cleaned before boiling. You can do this yourself or ask your fishmonger to do it. Cleaning involves removing the ink sac and the section of the head with the eyes, beak, and internal organs.