Prepare a charcoal grill for high-heat cooking, arranging the hot coals over one side of the grill. Alternatively, preheat all burners of a gas grill to high.

Set the cooking grate in place, cover, and preheat the grill for approximately 5 minutes.

Clean the grill grate thoroughly and lightly oil it to help prevent sticking.

Meanwhile, pat the cleaned squid completely dry with paper towels. Removing excess surface moisture helps the squid brown rather than steam.

Place the squid in a medium bowl and drizzle lightly with extra-virgin olive oil. Toss until evenly coated.

Arrange the squid directly over the hottest section of the grill without overcrowding.

Grill briefly, turning once, until both sides develop attractive browning and light char marks and the squid is opaque and just cooked through. Depending on size and grill temperature, this generally takes only a few minutes.

Immediately transfer the Grilled Squid to a serving platter.

Season with kosher salt and freshly ground black pepper.

Drizzle with a little fresh extra-virgin olive oil and sprinkle generously with chopped parsley.

Serve immediately with fresh lemon wedges on the side.