Cut onion in half lengthwise; cut each half into 1/4-inch slices. Cut green beans into 1/2-inch pieces; cut carrots and celery into 1/8-inch slices. Set aside.
Stir together soy sauce and 1 tablespoon cornstarch. Add chicken, stirring to coat.
Heat 1 tablespoon oil in a large skillet; add chicken, and stir-fry 1 to 2 minutes. Remove chicken, and set aside.
Add remaining 2 tablespoons oil to skillet. Add vegetables and garlic; cook, covered, 1 minute, shaking skillet to keep vegetables from sticking. Uncover; cook, stirring constantly, 2 to 4 minutes.
Stir together broth and 1 teaspoon cornstarch. Add chicken and broth mixture to vegetables; stir until thickened. Stir in cashews.
Stir-fry Beef: Substitute 1/2 pound top sirloin steak for chicken, and cut into 1/8-inch strips. Omit cashews.
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