Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with cooking spray or a thin layer of oil.
Heat vegetable oil in a large skillet over medium heat. Add diced onions and cook until translucent, about 3-4 minutes.
Add minced garlic and grated ginger, cooking for another 30 seconds until fragrant.
Add chicken pieces to the skillet and cook until the outsides are golden brown, about 5-7 minutes.
Pour teriyaki sauce over the chicken mixture and bring to a gentle simmer. Let it bubble for about 2 minutes. If your sauce seems too thick, you can add 2-3 tablespoons of water or chicken broth.
Spread cooked rice evenly in the bottom of your prepared baking dish. Layer the mixed vegetables over the rice, then pour the teriyaki chicken mixture on top. If using pineapple chunks, distribute them evenly throughout the dish.
Cover the baking dish with aluminum foil and bake for 25 minutes. Then remove the foil and bake for an additional 10 minutes until the top is slightly crispy and the casserole is bubbling around the edges.
Remove from oven and let stand for 5 minutes before serving. Sprinkle with sliced green onions and sesame seeds.