Begin by boiling a large pot of salted water. Add the octopus and simmer for about 45 minutes, or until tender. You can test for doneness by piercing the thickest part with a fork; it should slide in easily.

Once cooked, remove the octopus from the pot and let it cool slightly. When cool enough to handle, cut the tentacles from the body and discard the body.

In a bowl, whisk together the olive oil, lemon juice, minced garlic, oregano, smoked paprika, salt, and pepper. Add the octopus tentacles to the marinade and let them soak for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.

Preheat your grill to medium-high heat.

Remove the octopus from the marinade and place it on the grill. Grill for about 3-4 minutes on each side, or until you see nice grill marks and the tentacles are slightly charred.

Remove the octopus from the grill and let it rest for a few minutes. Slice the tentacles into bite-sized pieces.

Serve the grilled octopus garnished with fresh parsley and lemon wedges on the side.