To prepare vinaigrette, combine first 7 ingredients in a small bowl; stir with a whisk. Set aside.
To prepare salad, combine orange sections, romaine, red leaf lettuce, and spinach in a large bowl. Add onion and cheese. Pour vinaigrette over salad mixture; toss gently to coat.
You'll find the best oranges during the winter months. Mix the vinaigrette and prepare greens up to two days in advance, storing each component separately until it's time to toss the salad. Keep greens chilled and covered with a damp towel.