Slice meat into 3-inch strips, 1/8-inch thick. Mix all ingredients for sauce, except brown sugar and cornstarch. Marinate beef strips in sauce 3 hours or overnight in refrigerator. Drain, reserving sauce.
Weave beef strips back and forth on skewers. Brush with sauce. Preheat grill. Arrange skewers on grill and grill 8-12 minutes, turning occasionally. In saucepan; stir brown sugar and cornstarch into remaining sauce; bring to boil, stirring constantly until thickened.
Serve thickened sauce over skewers on a bed of rice.