Simmer the octopus: Place the cleaned octopus in a large pot and cover with water. Bring to a gentle simmer and cook for 45–60 minutes or until tender when pierced with a fork.
Remove from water and let cool slightly. Pat dry thoroughly.
In a small bowl, mix olive oil, minced garlic, lemon juice, oregano, salt, and pepper.
Brush the octopus generously with the marinade.
Preheat grill to medium-high heat.
Grill octopus for 3–4 minutes per side, brushing with more marinade as it cooks.
Remove from grill and let rest for a few minutes.
Slice tentacles if serving individually.
Garnish with chopped parsley and serve with lemon wedges.