Heat barbecue to high. Coat green onions with 1 tsp (5 mL) olive oil and grill about 1 min. per side or until lightly charred. Cool and finely chop.
In a bowl, mix cheese, pesto, pepper and green onion. Set aside.
Brush both sides of the steaks with the remaining olive oil and season with salt. Grill over medium-high heat for 1 to 2 min., just until grill marks form. Turn to sear the other side. Move steaks away from the hottest part of grill and continue cooking about 7 min. for medium (160°F/71°C on an instant-read thermometer). Remove steaks from grill and let rest 5 to 10 min. before serving. Top with 1 to 2 tbsp (15 to 30 mL) of the cheese mixture and serve.
For a more tender steak, let the meat rest 30 minutes at room temperature before grilling.