Fill a medium-sized container or pot with water, attach the sous vide precision cooker and set the temperature to 171ºF (77ºC).
Wash and clean the octopus, and remove the ink sac and internal organs. Pull away the beak.
Lightly season the octopus with salt, pepper, and half tablespoon oil.
Place the octopus in in a large zip-top bag or vacuum seal bag. (If your octopus is really big, you can cut it into smaller portions and use multiple bags if necessary).
Seal the bag using the “water displacement” technique: seal all but one corner of the bag and slowly place it in the water bath. Make sure everything below the zip-line is covered by water. Then seal the rest of the bag. (Use a vacuum sealer if you have one.)
Once the temperature has reached 171ºF (77ºC), place the sealed bag in the water bath and set the timer for 5 hours. Make sure to submerge the octopus completely in the water.
When the time goes off, remove the bag from the water bath and transfer to an ice bath. Leave for 15 minutes (or you can chill them in the refrigerator for about 1 hour).
Once the octopus are chilled, pat dry with paper towels (wet octopus won’t sear properly).
On a very hot grill or a large skillet, brush with the rest of the oil, sear the octopus for 2-3 minutes each side (4-5 minutes in total) until nicely browned. Remove from the grill or skillet and transfer to a place.
In a small bowl, whisk together melted butter, lemon juice, salt, and pepper. Season to taste.
Drizzle the octopus with the mixture and garnish with parsley if desired.