Cook the quinoa according to package directions, set aside to cool.
Heat the vegetable oil in a small saucepan over medium heat. When the oil is hot, add the ginger, scallions and garlic. Immediately turn off the heat and stir. Let cool slightly for a few minutes, then whisk in the lemon juice, soy sauce and sesame oil.
Put the cooked quinoa, chicken, cabbage, carrots and peas in a mixing bowl. Add the dressing and toss. Sprinkle with sesame seeds. Keep refrigerated in an air-tight container for up to 3 days.