Grilled Baby Octopus with Roasted Peppers and Potatoes

In a medium saucepan, heat 1/4 cup of the olive oil. Add the chopped garlic and shallots and cook over moderately high heat, stirring a few times, until golden brown, about 4 minutes. Add the octopus, the remaining 2 cups of olive oil and a pinch of salt and bring to a simmer. Cook over low heat, skimming a few times, until the octopus is tender, about 45 minutes. Using tongs, transfer the octopus to a large plate and cover with plastic wrap. Strain and reserve 1/2 cup of the olive oil.

Roast the bell peppers over a gas flame or under a preheated broiler, turning, until they are charred all over. Transfer the roasted peppers to a large plate and let cool, then rub off the skins and discard the seeds. Slice the roasted peppers into thin strips.

In a medium saucepan, cover the cubed potatoes with water by 3 inches and boil over moderately high heat until tender, about 10 minutes. Drain the potatoes and return them to the pan. Shake the saucepan over the heat for about 10 seconds to dry out the potatoes.

In a large skillet, heat 2 tablespoons of the reserved octopus oil. Add the sliced garlic and shallot and cook over moderately high heat until softened, about 2 minutes. Add the roasted pepper strips and the 1/2 teaspoon of paprika and cook, stirring, until the peppers are hot. Add the potatoes and cook, tossing gently, until heated through. Drizzle the roasted pepper–potato salad with 1/2 tablespoon of the lemon juice and season with salt and freshly ground black pepper.

Light a grill or heat a grill pan. Brush the octopus with some of the reserved octopus oil and season with salt and black pepper. Grill over high heat, turning once, until the octopus are nicely charred and crisp, about 3 minutes per side.

Arrange the roasted pepper–potato salad on a platter and top with the grilled octopus. Drizzle with the remaining reserved octopus oil and the remaining 1 tablespoon of lemon juice. Sprinkle with smoked paprika and the chopped parsley and serve.