Make the dressing: Whisk together ginger, garlic, lime juice, vinegar, sesame oil, and sugar in a small bowl. Gradually add olive oil, whisking constantly until fully combined. Set aside.
Remove peel and pith from grapefruit. Holding over a medium bowl, carve out flesh between the membranes, letting segments drop into the bowl (you should have about 3/4 cup segments). Add watercress. Pour dressing over watercress and grapefruit; toss to coat. Sprinkle with walnuts. Season with salt and pepper.