Season sliced chicken lightly with salt and black pepper.
Heat 1 tablespoon oil in a wok or large skillet over medium-high heat. Add chicken and cook until lightly golden and cooked through. Remove and set aside.
Add remaining oil to the pan and stir fry broccoli for 3–4 minutes until bright green and just tender.
In a small bowl, whisk together soy sauce, garlic, ginger, chicken broth, cornstarch, and sesame oil.
Return chicken to the pan, pour in the sauce, and cook while stirring until the sauce thickens and coats everything evenly.
Serve immediately.