Preheat the grill or grill pan over medium-high heat.
Add octopus tentacles, lemon juice, and olive oil in a bowl. Let the tentacles stand for 10 minutes.
Grill the octopus for 3-4 minutes per side. While it's grilling, whisk together the olive oil, salt, pepper, red pepper flakes, and garlic.
Remove the octopus tentacles from the grill and serve over arugula with the sauce drizzled on top.
Notes
TO STORE: Let the octopus cool completely, then store in an airtight container in the refrigerator for 3-4 days.TO FREEZE: Store the cooled octopus in a freezer-safe container for up to 3 months. Let them thaw completely before reheating. TO REHEAT: Reheat leftovers on the grill or stovetop over medium heat, flipping often, until warm.Recipe variations
Greek-inspired octopus. I find Greek flavors pair beautifully with octopus. Simply toss dried oregano, thyme, and bay leaves with the tentacles. Discard the bay leaves just before grilling. Then, serve it with sliced olives, feta cheese, and sliced tomatoes.
Garnish. Serve with a sprinkle of fresh herbs, like fresh parsley or cilantro.
Sauce. Top the octopus with a drizzle of spicy mayo or garlic yogurt sauce, or set it on the side so guests can help themselves.