Combine the rice and water in a small, heavy saucepan and bring to a boil. Stir, cover, reduce the heat to low, and cook until the rice is tender, 40 to 45 minutes. Bring a separate covered pot of water to a boil for blanching the vegetables.
Meanwhile, in a small nonreactive pan, combine the rice vinegar, sugar, salt, and ginger root; simmer for 5 minutes, and set aside.
When the water boils, blanch the carrots and then the peppers just until tender. In a serving bowl, combine the cucumbers, blanched vegetables, and sauce.
When the rice is done, toss the wasabi paste with the sauce and vegetables. Add the rice and toss to mix well. Serve the salad at room temperature or chilled.
Just before serving, toast the sheet of nori by briefly passing it over a low flame or baking it for a minute or so in a 300 degree F toaster oven, until it deepens in color. Crumble it into a small bowl.
Toast the sesame seeds. Spoon the rice salad onto individual beds of greens, sprinkle with sesame seeds and nori, and serve.