Cut the cooked octopus leg into chunks. In a non-reactive pan or zip top plastic bag combine the ¼ cup olive oil, lime juice, cilantro, jalapeño and cumin. Add octopus (or chicken breast or pork shops) and stir to coat completely. Refrigerate at least 1 hour or overnight.
Scrub potatoes with vegetable brush under cold running water. Place potatoes in large saucepan and add enough cold water to cover completely. Heat to boiling, and then reduce heat to simmer. Cover and cook until just tender, about 10 to 15 minutes. Let cool briefly. Peel.
In large bowl combine potatoes, sour cream, parsley, salt and pepper and mash with a fork until mixed but still a little lumpy. Form into 4 patties, each about 1 inch thick. Set aside.
Preheat a grill or cast iron grill pan. Lift octopus from marinade and grill on preheated grill until well browned on all sides. Place on plate, cover with foil and keep warm in 250° oven. In a large skillet over medium-high heat, heat the 1 tablespoon olive oil. Add patties and reduce heat to medium. Cook until lightly browned, about 4 minutes. Turn and brown the second side, about 4 minutes. Place one potato patty on each plate and top with pieces of grilled octopus.
Nutritional Analysis per serving: 761 calories, 55 g protein, 37 g carbohydrates, 42 g fat (51% of calories from fat), 170 mg cholesterol, 2 g fiber, 1282 mg sodium.