To prepare the vinaigrette, combine the first 9 ingredients in a small bowl; stir well with a whisk, and set aside.
To prepare the salad, bring the water and ginger slice to a simmer in a large saucepan; add broccoli florets. Cook 1 minute. Add the cabbage, green onions, and snow peas; cook 30 seconds. Drain and rinse with cold water; drain well. Place the cabbage mixture on several layers of paper towels, and cover with additional paper towels. Let stand 5 minutes, pressing down occasionally. Combine broccoli mixture, tofu, sesame seeds, salt, and pepper in a large bowl. Add vinaigrette, tossing to coat.