Boil the Octopus: In a large pot with plenty of boiling water, add the whole octopus. Enrich the water with onion, garlic, thyme, bay leaf, and black pepper. Leave the pot ajar and cook for 30 minutes per kilo of octopus.
Check for Doneness: Take the octopus out of the pot. Use a fork to check if it's ready by sticking it in the base of a tentacle; if it goes in with ease, the octopus is ready.
Cut and Season: Cut the tentacles and season them with salt and black pepper.
Grill the Octopus: In a frying pan over medium heat, add olive oil and grill the octopus until one side is done. Then, turn the heat down, add butter, thyme, garlic, and a little lemon juice. Continue grilling until golden brown.
Serve: Serve the octopus hot. Optionally, use the broth left in the pot to make a flavorful rice.