Wash the potatoes and brush off the dirt. Place in a saucepan, fill with water and cook until soft. Drain, peel, cut in cubes and set aside. Keep them warm.
Cut the cherry tomatoes in half.
Pierce each small octopus with long wood sticks. This will allow you to curl the tentacles without getting burnt.
In a deep casserole cook 2 cloves of crushed garlic and the bay leaf in 2 tablespoons of oil until golden. Turn up the heat and add the little octopus, one at the time, holding from the stick. Lay the tentacles first, once curled, leave the whole octopus. Cover and cook for 10 to 15 minutes. The octopus will be ready once piercing the neck, the meat feels tender. Season with salt. Remove the octopus from the pan and set aside. Reserve the cooking liquid.
In a saucepan cook the remaining 2 cloves of garlic in 3 tablespoons of oil. Once golden, add the tomatoes, basil, salt and cook for 5 to 6 minutes. Do not stir.
When the tomatoes start to soften up, stir vigorously and crush pushing them against the sides of the pan. You'll get a creamy sauce. remove from heat and transfer to a strainer.
With a spoon, crush the tomatoes against the strainer and collect the pulp and sauce in a container. Discard garlic and tomatoes skin.
In a blender place the octopus cooking liquid set aside and the tomato sauce. Adjust with seasoning and blend to have a smooth sauce.
Assemble the dish, pour a ladle of tomato sauce on the bottom of 4 soup bowls, add some sauteed octopus and few potato cubes. Sprinkle with parsley and drizzle with some extra virgin olive oil. Serve.