In a medium saucepan with a tight-fitting lid, mix the chicken broth with the white and light green scallion slices and the spinach. Cook, covered, over medium-high heat, removing the lid a few times to break up the spinach with a wooden spoon, until thawed. Bring the soup to a boil, about 10 minutes. Reduce the heat to medium-low, add the tofu without stirring and cook until heated through, 2 to 3 minutes. Remove the pan from the heat, add the dark green scallion slices and the sesame oil and season to taste with salt and pepper.