Preheat your oven to 375°F (190°C) and lightly grease a 9x13-inch baking dish with non-stick cooking spray.

In the prepared baking dish, spread the rinsed uncooked jasmine rice in an even layer across the bottom. Pour the chicken broth over the rice, ensuring all the grains are fully submerged.

Scatter the diced chicken breasts, minced garlic, and shredded carrots evenly over the rice and broth mixture.

Pour the thick teriyaki sauce evenly over the chicken and vegetables. Cover the baking dish tightly with aluminum foil to trap the steam, which is essential for cooking the rice and chicken.

Bake in the preheated oven for 35 minutes. Carefully remove the foil and check that the rice is mostly tender and the chicken is fully cooked through with no pink remaining.

Stir the mixture gently, then fold in the fresh broccoli florets. Return the casserole to the oven, uncovered, and bake for an additional 10 to 15 minutes, or until the broccoli is tender-crisp and the sauce has thickened nicely.

Remove the casserole from the oven and let it rest for 5 minutes before serving. Garnish generously with sliced green onions and toasted sesame seeds, and serve hot directly from the dish.