Clean octopus, it it was bought previously frozen, it will most likely not require cleaning.
Bring a large bot of water to a boil. Add octopus. Boil for 15 minutes, then add potatoes.
Boil for about 30 more minutes. Remove the octopus and cut a piece to test doneness. If it appears too dense and chewy, boil for another 5-10 minutes.
Carefully remove the potatoes.
Cut the tentacles of the octopus.
Heat 1 tbsp olive oil in a grill skillet over medium heat. Add octopus. Cook for 2 minutes per side, turning once (total of 4 minutes). Remove and transfer to a plate.
Cut potatoes onto bite sized pieces. Arrange on a plate.
Add octopus on top. Season with salt, pepper and paprika.
Drizzle with olive oil and vinegar (or lemon juice). Top with parsley. Serve immediately.