In a small bowl, whisk together rice vinegar, soy sauce, sesame oil, sugar, garlic, and ginger until sugar dissolves. Set aside.
Slice the cucumber into half-moons about 1/4-inch thick. If using regular cucumbers, peel if skin is tough.
In a large bowl, combine the cooled rice, cucumber slices, and green onions.
Pour the dressing over the salad and toss gently to coat.
Let the salad sit at room temperature for 15 minutes, or cover and refrigerate for at least 30 minutes for deeper flavor.
Sprinkle with sesame seeds just before serving. Serve cold or at room temperature.