Prepare all ingredients as instructed above.
Make the Iced Ginger Tea: Bring water to a simmer in a small pot. Remove from heat and steep ginger tea bags for 10 minutes.
Sweeten with sugar or honey to taste. Remove tea bags, let cool, and refrigerate until ready to serve over ice.
Cook the Rice: Rinse rice thoroughly under cold water. Cook according to package instructions. Fluff with a fork, season with salt and pepper, and keep warm.
Prepare the Teriyaki Sauce: In a small bowl, combine soy sauce, rice wine vinegar, sake, and brown sugar. Mix well and set aside.
Cook the Chicken: Season diced chicken with salt and black pepper. Heat vegetable oil in a large skillet over medium heat.
Add chicken and cook until browned on all sides.
Pour teriyaki sauce over the chicken. Reduce heat to medium-low and simmer for about 5 minutes, or until sauce thickens.
Cook the Broccolini: Bring a pot of water to a boil. Add broccolini and cook until tender, about 3–5 minutes. Drain and season with salt and pepper.
Serve: Plate the chicken teriyaki over rice. Garnish with scallions and sesame seeds. Serve with broccolini, iced ginger tea, and fortune cookies.