Place basil leaves in plastic bag and mash to release flavors and oils. Add two tablespoons olive oil, soy sauce, brown sugar, pepper, and beef into bag; refrigerate overnight.
Warm a non-stick skillet over medium heat; add remaining oil when hot. Toss garlic and green onion in oil for two or three minutes, being careful not to brown them. Add marinated beef; sauté for 3-4 minutes until cooked as desired, monitoring closely.