Whisk together soy sauce and cornstarch in a medium bowl. Add chicken, stir to coat, and set aside.
Heat oil in a wok or large skillet over high heat. Add chicken mixture, season with salt and pepper, and stir-fry until no longer pink, about 2 minutes. Remove from the pan and set aside.
Add ginger and garlic and cook, stirring constantly, for 30 seconds without browning. Add asparagus and stir-fry for 1.
Stir in broth, cover, reduce heat to medium-low and cook until asparagus is crisp tender, about 2 minutes. Return chicken to pan and stir-fry to reheat, about 1 minute. Drizzle a little sesame oil over and serve immediately.