Arrange a lettuce leaf on each dinner plate. Cut steak in half lengthwise, then cut across the grain into 1/8-in. slices.
In a heavy skillet, heat oil over medium-high heat. Add beef, basil, garlic and pepper. Stir-fry just until meat loses pink color, about 2 minutes. Remove from the heat. Add the tomatoes, green pepper and green onions; toss lightly.
Transfer beef and vegetables to dinner plates; top with sour cream and parsley. Garnish with avocado.