Divide the cooled quinoa or rice between two bowls as the base.
In a small bowl, whisk together the teriyaki sauce, lime juice, and sesame oil until combined. Set aside.
Arrange the cucumber, carrot ribbons, and scallions over the grain base.
Break the smoked salmon into large flakes with a fork and scatter it over the vegetables.
Add the avocado slices, tucking them in among the other vegetables.
Drizzle the teriyaki dressing evenly over both bowls just before serving.
Sprinkle with sesame seeds and serve immediately.