Toss chicken with 1 tablespoon cornstarch. In a small bowl, whisk together broth, vinegar, sugar, garlic chili sauce, soy sauce, and remaining cornstarch; set aside.
In a large nonstick skillet, heat oil over medium-high. Saute chicken until golden brown and cooked through, 8 to 10 minutes; remove chicken and set aside. Add leek, jicama, bell pepper, ginger, and garlic; cook, stirring frequently until jicama is crisp-tender, about 3 minutes. Return chicken to pan along with watercress; cook until watercress has wilted, about 2 minutes.
Whisk soy sauce mixture, then add to pan. Bring to a simmer and cook, stirring constantly until the sauce has thickened, about 1 minute. Serve immediately.