Preheat the oven to 300°F (150°C).
Clean the octopus by removing the head and beak, and rinsing thoroughly.
In a large pot, bring water to a boil and add the octopus. Cook for about 45 minutes to 1 hour, or until tender. Drain and let cool.
Preheat the oven to 400°F (200°C).
In a small bowl, combine the olive oil, za'atar spice, lemon juice, salt, and pepper.
Rub the octopus with the za'atar mixture to coat evenly.
Place the octopus on a baking sheet and roast in the oven for about 30-40 minutes, or until crispy and golden brown.
Remove from the oven and let cool for a few minutes before serving.
Serve the oven-roasted za'atar octopus with lemon wedges and enjoy!