Pat the octopus tentacles dry with paper towels and cut them into 1-inch bite-sized pieces.
Place the pieces in a bowl and toss with 2 tablespoons olive oil, 1 teaspoon smoked paprika, salt, and black pepper until evenly coated.
Heat the remaining tablespoon of olive oil in a large skillet over medium-high heat. Add the octopus pieces in a single layer and cook undisturbed for 2-3 minutes per side until charred and crisp at the edges.
While the octopus cooks, make the aioli. Stir the mayonnaise, mashed black garlic, lemon juice, and remaining teaspoon of smoked paprika together in a small bowl until smooth.
Transfer the charred bites to a serving plate and serve immediately with the black garlic aioli on the side for dipping.