How to Make It
In a large pot, bring 8 quarts of water to a boil. Add the salt, peppercorns, bay leaf and the penny. Holding the octopus by the head, carefully and quickly dip the tentacles into the water 3 times, then lower it into the pot. Reduce the heat to moderately low and simmer until almost tender, about 1 hour and 15 minutes. If necessary, place a plate over the octopus to keep it submerged.
Add the potatoes and cook until the octopus and potatoes are tender, about 25 minutes more. Transfer the octopus and potatoes to a work surface; discard the braising liquid. Separate the tentacles and cut the head in half. Using a paper towel, wipe the purple skin off the tentacles, leaving the suckers intact. Thinly slice the potatoes and arrange on a platter.
Light a grill or preheat a grill pan. Brush the octopus with the 3 tablespoons of olive oil. Grill over moderately high heat, turning, until lightly charred, about 4 minutes. Arrange the octopus on the platter with the potatoes. Drizzle with the lemon juice and more olive oil. Sprinkle with the paprika, flaky sea salt and parsley leaves; serve.
Andrés adds a clean penny to the saucepan to replicate the traditional technique of cooking octopus in a copper pot. Soak the penny in distilled white vinegar and salt for 10 minutes, then scrub it clean before using.