If necessary, clean the baby squid by removing the internal organs, transparent cartilage, eyes, and beak. Rinse briefly and pat completely dry with paper towels.
Place the squid in a bowl. Add the olive oil, garlic, 2 tablespoons of parsley, lemon zest, salt, and black pepper. Toss well to coat.
Let the squid marinate at room temperature for 15–20 minutes.
Preheat an outdoor grill or grill pan over high heat. Lightly oil the grates if necessary.
Remove the squid from the marinade and let the excess oil drip off. Arrange the squid on the hot grill in a single layer.
Grill for 1–2 minutes per side, until the squid is opaque, lightly charred, and curled around the edges. Cook it in batches to avoid overcrowding.
Transfer the squid to a serving plate. Drizzle with a little extra-virgin olive oil and sprinkle with the remaining parsley.
Serve immediately with fresh lemon wedges.