Fill a medium saucepan with cold water and the sliced potatoes. Set over moderate heat and bring to a boil. Cook until just fork tender, about 8 to 10 minutes. During the last 2 minutes of cooking, add the green beans to the pot and continue to cook for the remaining time. Drain in a colander and set aside to cool.
Drizzle the octopus with olive oil and season lightly with salt and pepper on both sides.
Set a grill pan over medium-high and grease with cooking spray or oil. Once hot, place the seasoned octopus on, in a single layer, and cook until charred on both sides, about 4 to 6 minutes per side. Transfer to a cutting board and set aside to cool slightly before slicing into 1/4-inch rounds.
To make the dressing, in a large glass measuring cup, whisk together the vinegar, oil, mustard, garlic, basil, red pepper, and a large pinch of salt and pepper until evenly combined and well-emulsified. Give it a taste and adjust seasoning accordingly.
To assemble the salad, in a large mixing bowl, combine the cooled potatoes, green beans, tomatoes, shallot, olives, parsley, lemon juice, octopus and a pinch of salt and pepper. Drizzle in about half of the dressing and toss to evenly combine. Transfer to a serving platter and drizzle with more of the remaining dressing. Serve immediately and enjoy!