Beef Stir-Fry with Arugula

In nonstick 12-inch skillet, heat 2 teaspoons oil over medium-high heat. Add green onions and mushrooms and cook until tender and brown, about 5 minutes, stirring often. Remove to bowl. In same skillet, heat 1 teaspoon oil. Add half the beef and cook, stirring constantly, until beef just loses its pink color. Remove to bowl with vegetables. Cook remaining beef as above, adding remaining 1 teaspoon oil. In cup, mix soy sauce, balsamic vinegar, and brown sugar. Return beef mixture to skillet; stir in soy-sauce mixture. Cook 1 minute to heat through, stirring. Remove from heat; stir in half the arugula. Spoon beef mixture over remaining arugula on platter.