Combine flank steak, 3 tablespoons of olive oil, garlic, 2 tablespoons lime juice, cilantro, salt, pepper, and 1/4 cup chopped green onions in a large zip-top plastic bag. Allow steak to marinate at room temperature for 45 minutes, turning occasionally. Alternatively, marinate in the refrigerator overnight.
Preheat grill to medium-high.
Remove steak from marinade bag and remove as much of the marinade as possible. Discard remaining marinade. Place the steak on the preheated grill and cook steak for 2 1/2 minutes, then rotate on same side 45 degrees (to create grill marks) and grill for another 2 1/2 minutes. Flip steak and cook for an additional 5 minutes on the other side, rotating 45 degrees after 2 1/2 minutes. Remove from grill pan and allow the steak to rest for 10 minutes under a foil tent.
Meanwhile, trim the root ends of the green onions and toss with the remaining tablespoon of olive oil and salt, to season. Place the green onions on the grill and cook for 1 1/2 to 2 minutes, (depending on the size of the onions), or until softened and slightly charred. Remove the onions from the grill and toss with the remaining 2 tablespoons of lime juice.
Slice the steak against the grain as thinly as possible and divide evenly between 4 plates. Drizzle with extra-virgin olive oil. Top each steak with several grilled onions. Garnish each plate with fresh cilantro sprigs and a lime wedge.