Place the cleaned octopus tentacles in a large pot and add the white wine, garlic, a pinch of salt, and black pepper. Bring to a boil over medium-high heat, then reduce to a gentle simmer. Cook for about 45 minutes until the tentacles are tender when pierced with a fork.
Remove the octopus from the liquid and let it cool slightly until manageable. Pat dry with paper towels to remove excess moisture, which helps achieve a good sear.
Preheat the grill to high heat, aiming for around 450°F (232°C). Brush the octopus tentacles with olive oil to promote crisping and prevent sticking.
Place the tentacles directly on the hot grill grates. Grill for 4-5 minutes per side, watching for a deep, smoky char to develop and listening for sizzling and crackling sounds.
Use tongs to flip the tentacles and continue grilling until both sides are evenly charred and crispy on the edges.
Remove the grilled octopus from the heat and transfer to a serving plate. Squeeze fresh lemon juice over the top for brightness and flavor.
Slice the tentacles into smaller pieces if desired and serve immediately, enjoying the contrast of smoky, crispy exterior and tender interior.
