1. In a medium bowl, whisk together oil, rice vinegar, sugar, salt and ground ginger until blended and oil is well-incorporated and emulsified.
2. Reserve 1 cup of dressing; cover and refrigerate.
3. Drizzle 1/4 cup of dressing on mushrooms. Grill mushrooms directly over medium heat 10 to 15 minutes, turning several times.
4. Season salmon with salt and pepper. Lightly brush salmon with remaining 1/4 cup of dressing to avoid sticking to grill grates. Grill salmon directly over medium heat 8 to 10 minutes, turning once halfway through cooking time.
5. Slice portabella mushrooms into strips and place on serving plates as a bed for salmon. Top mushrooms with grilled salmon. Drizzle refrigerated dressing generously over salmon and mushrooms.