Whisk cranberry sauce, vinegar, grated orange zest, orange juice, sesame oil, and 2 tbsp soy sauce in a small bowl until jelly is mostly dissolved
Toss chicken, cornstarch, and remaining 1 tbsp soy sauce in a medium bowl until chicken is well-coated
Heat 2 tbsp vegetable oil in a large skillet or wok over high heat. Cook green beans, tossing very occasionally, until tender and deeply browned in spots, about 6-8 minutes. Use tongs to transfer to a bowl
Add remaining 2 tbsp to the same skillet or wok and arrange chicken in a single layer. Cook, tossing occasionally, until golden brown and cooked through, about 5 minutes. Transfer to bowl with green beans
If pan is dry, add more vegetable oil (up to 2 tbsp). Add garlic and ginger and cook, stirring constantly, until fragrant, about 1 minute. Add reserved sauce and cook until slightly thickened, about 2-3 minutes. Add green beans and chicken and toss to coat. Salt to taste
Put in bowls with white rice and garnish with sliced orange zest and sesame seeds