Place onion, garlic, bay leaves, paprika, salt, and 1 tablespoon olive oil into a 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.
Place octopus into braising liquid, turning to coat with the liquid. Cover; reduce heat to low. Simmer for 20 minutes and turn octopus over. Continue cooking until octopus is tender, another 30 to 45 minutes.
Remove from heat; transfer octopus to a large bowl. Pour braising liquid over octopus. Place bowl in a bowl of ice water to cool to room temperature. Cover bowl with plastic wrap when octopus and liquid are cool. Refrigerate until thoroughly chilled, at least 2 hours or overnight.
Transfer octopus to a work surface and pat dry with paper towels. Cut octopus into 3 or 4 serving-size pieces. Brush with remaining 2 tablespoons olive oil.
Transfer ⅓ cup braising liquid to saucepan. Bring to a boil over medium heat; remove from heat. Strain out solids; transfer liquid to a mixing bowl, and let cool for about 10 minutes. Stir in orange and lemon zests, lemon juice, extra-virgin olive oil, salt, and cayenne pepper to make the serving sauce.
Heat grill to high heat. Place octopus pieces on 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. 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. Garnish with parsley and lemon slices, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/chef-folses-spanish-style-grilled-octopus/