Trim stems and any yellow leaves from Brussels sprouts. Cut each sprout lengthwise into quarters. In cup, stir together soy sauce, grated ginger, and sesame oil.
Meanwhile, in nonstick 12-inch skillet, heat olive oil over medium heat until hot. Add onion and cook about 5 mintues or until it begins to soften, stirring occasionally.
Increase heat to medium-high; add Brussels sprouts and water; cover and cook about 5 minutes or until sprouts are beginning to soften and brown, stirring once. Remove cover from skillet and cook about 5 minutes longer or until sprouts are tender-crisp, stirring frequently. Remove skillte from heat; stir in a soy sauce mixture.