Cut squid bodies along sides to open flat. With a thin, sharp knife, lightly score insides, being careful not to cut all the way through.

In a bowl, combine 2 tablespoons olive oil, lemon juice, garlic, and salt. Add the calamari and toss to coat. Allow calamari to marinate up to 10 minutes while you preheat the grill to high heat.

Grill squid, turning occasionally, until opaque, slightly golden, and just cooked through, about 2 to 3 minutes. Take care to not overcook. Remove squid to cutting board and slice into strips. Slice tentacles if desired.

Lightly drizzle with additional extra virgin olive oil as desired, sprinkle with salt if desired, and parsley, and serve with the lemon wedges on the side.