Step 1
Place chopped onion garlic cloves bay leaf paprika salt and 1 tablespoon olive oil into saucepan. Cook and stir over medium-high heat until onions start to soften about 5 minutes. Add white wine to create the braising liquid. Bring to a simmer.
Step 2
Transfer octopus into braising liquid turning to coat with the liquid. Cover; reduce heat to low. Simmer 20 minutes and turn octopus over. Continue cooking until octopus is tender another 40 to 45 minutes.
Step 3
Remove from heat; transfer octopus to a large bowl. Pour braising liquid over octopus. Place bowl above a bowl of ice water to cool to room temperature.
Step 4
Cover bowl with plastic wrap when octopus and liquid are cool. Refrigerate until thoroughly chilled at least 2 hours or overnight.
Step 5
Transfer octopus to a work surface and mop off braising juices with paper towels; remove as much of the purple skin as you want. Cut octopus into 3 or 4 serving-size pieces. Brush with olive oil.
Step 6
Transfer braising liquid to saucepan. Bring to a boil; remove from heat. Strain out solids; transfer liquid to a mixing bowl; let cool about 10 minutes. Stir in lemon juice extra-virgin olive oil parsley salt and cayenne pepper to make the serving sauce.
Step 7
Heat a grill pan or outdoor grill to high heat. Transfer octopus pieces to grill. Cook until flesh is seared almost charred 3 or 4 minutes. Turn and cook other side until dark brown caramelized and heated through another 3 or 4 minutes. Transfer to a platter.
Step 8
Slice octopus into fairly thick diagonal slices. Place on a serving dish. Spoon braising liquid mixture over the top. Dust with a bit of cayenne pepper if desired.