In a large pot, heat sesame oil. Stir in the chopped onion and garlic; cook and stir until the onion has softened and turned translucent, about 5 minutes. Pour in the chicken broth and green onions. Bring to a boil over high heat, and season to taste with salt and pepper.
Reduce the heat to medium, and add the frozen pot stickers and mixed vegetables. Cook until the pot stickers float, about 8 minutes.