Combine greens in a large bowl. Rub with sugar and 1 teaspoon salt until slightly damp. Refrigerate 30 to 60 minutes.
In a small bowl, whisk together vinegar, mustard, soy sauce, and remaining 1 teaspoon salt. Slowly whisk in oil. Toss greens with three-quarters of dressing. Add cheese and walnuts; toss to combine. Refrigerate at least 10 minutes and up to 1 hour. Serve, tossing with more dressing if desired.