Combine first 5 ingredients in a small bowl, stirring well. Set aside.
Slice cucumber lengthwise into thin strips, using a vegetable peeler and applying firm pressure. (Reserve center core of cucumber for another use.) Set cucumber strips aside.
Coat a small nonstick skillet with cooking spray; place over medium heat until hot. Add steak and next 4 ingredients; saute 3 to 4 minutes or until steak is done. Set aside.
Combine lettuce and spinach; place evenly on 2 salad plates. Arrange cucumber strips, steak mixture, and nectarine wedges over salad greens. Drizzle vinegar mixture evenly over salads, and sprinkle with cheese.