Place octopus in a bowl, cover with boiling water, weight with a plate or pot cover, and let stand 20 to 30 minutes to defrost.
Drain octopus. Pat dry with butcher paper or kitchen towel.
Cut the octopus into 1-inch pieces.
Cover octopus with 1 quart of water. Add 3 tablespoons salt and boil 15 minutes over medium-high heat.
Drain again and pat dry.
Rub octopus with 2 tablespoons vegetable oil.
Brush a large grill with oil.
Grill octopus over medium heat, turning occasionally, until tender, about 25 minutes.
Whisk together ¼ cup oil, lemon juice, parsley, garlic, 2 teaspoons salt, and ½ teaspoon pepper.
Thoroughly tenderize octopus by bashing with a mallet or hammer. Or, if you’re in a real hurry, chop it fine with a knife.
Stir in ¼ cup chopped parsley and enough dressing to lightly coat the octopus. Season to taste with salt and pepper and serve.
Serving Suggestions: For a great appetizer, use the remaining dressing to marinate some quartered cherry tomatoes. Serve with grilled bread.