Prepare the Sauce: In a small bowl, whisk together the pomegranate molasses, soy sauce, honey, rice vinegar, sesame oil, grated ginger, and minced garlic.
Cook the Chicken: Heat the vegetable oil in a large skillet over medium-high heat. Add the chicken chunks and cook until browned on all sides, about 5-7 minutes.
Combine and Simmer: Pour the sauce over the chicken and stir to coat evenly. Reduce the heat to medium-low and simmer for about 10 minutes, or until the chicken is cooked through and the sauce has thickened slightly.
Thicken the Sauce: In a small bowl, mix the cornstarch with water to create a slurry. Add the slurry to the skillet and stir well. Continue to cook for another 2-3 minutes, until the sauce is thick and glossy.
Serve: Garnish with sliced green onions and sesame seeds. Serve hot over steamed rice or your favorite Asian side dish.