In a small bowl, whisk together rice vinegar, soy sauce, sesame oil, sugar, ginger, and salt until sugar dissolves.
In a large bowl, combine cooked rice, diced cucumber, edamame, and 2 tablespoons of sesame seeds.
Pour dressing over the rice mixture and toss gently until well combined.
Let the salad marinate at room temperature for 15 minutes (or refrigerate up to 2 hours) for flavors to meld.
Taste and adjust seasoning with extra salt or vinegar if needed.
Transfer to a serving bowl, sprinkle with remaining sesame seeds and sliced green onions. Serve cold or at room temperature.