Rinse the rice until the water runs clear, then cook it in 2 cups of water until fluffy. Set aside.
Heat olive oil in a large skillet or wok. Add the chicken pieces and season lightly with salt and pepper. Cook until golden brown.
In a small bowl, whisk together soy sauce, teriyaki sauce, honey, garlic, ginger, and sesame oil.
Pour the sauce over the chicken and stir well until coated. Let it simmer for 5 minutes.
Add the broccoli florets and cook until they are bright green and slightly tender, about 3–4 minutes.
Serve the chicken and broccoli over the cooked rice. Sprinkle with sesame seeds and sliced spring onions before serving.