1 (2 1/2-pound; 1kg) whole cooked octopus, chilled, drained of cooking liquid, cleaned of eyes and beak, and dried thoroughly (see note)
1/2 cup (120ml) extra-virgin olive oil, plus more for drizzling
2 teaspoons (10ml) crushed or minced Calabrian chiles in oil, or a coarse chili paste such as sambal oelek
1 teaspoon minced fresh oregano leaves
Kosher salt
Lemon wedges, for serving
Frisée or other leafy greens, for serving
Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over half of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate.
In a medium bowl, stir together olive oil, chiles, and oregano. Season lightly with salt and set aside. The sauce can be held at room temperature for up to 5 hours; refrigerate if storing longer and return to room temperature before using.
If you want to grill the octopus whole, leave it as-is. Alternatively, you can break the octopus down into parts, separating the head from the tentacles (you will already have cut out the eyes and beak where they meet); you can then leave the tentacles in sections, or separate them all into individual pieces.
When ready to grill, lightly drizzle olive oil all over the octopus and season lightly with salt. Set on grill directly over the coals and sear until browned and crisped, about 4 minutes (grilling time will vary depending on the heat of your coals and distance between them and the grill grate.) Carefully flip octopus and brown the other side, about 4 minutes longer. Transfer to serving plates or platters if you want to serve the pieces as-is, or transfer them to a work surface if you want to cut them into smaller pieces, then arrange on serving plates.