Rinse the rice, then cook according to the package instructions. Fluff with a fork; set aside and keep warm.
While the rice is cooking, prepare the teriyaki sauce. In a bowl, mix together soy sauce, rice wine (or mirin), sake, and brown sugar. Set aside.
Cut the chicken breasts into bite-sized pieces. Salt and pepper the chicken.
Heat vegetable oil in a large skillet over medium-high heat.
Add the chicken to the skillet and cook until browned on all sides.
Pour the teriyaki sauce over the chicken, reduce heat to medium, and let it simmer until the sauce thickens and coats the chicken (about 5-7 minutes).
In the last 3 minutes of cooking, add broccoli florets to the skillet and cook until they are tender-crisp.
Optional: Drizzle sesame oil over the chicken and broccoli for extra flavor.
Serve the teriyaki chicken and broccoli over the cooked jasmine rice. Garnish with sliced scallions and sesame seeds. Enjoy with a glass of sweet iced tea.