Cook jasmine rice according to package directions so it's ready when the stir fry is done.
In a small bowl, whisk together soy sauce, mirin, sake, and brown sugar. In a separate tiny bowl, mix cornstarch and water to create a slurry. Set both aside.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Working in batches if needed, add sliced beef in a single layer and sear for 1–2 minutes per side until browned but not fully cooked through. Transfer to a plate.
Reduce heat to medium. In the same skillet, add a tiny splash more oil if needed, then add garlic and ginger, stirring for 30 seconds until fragrant. Toss in broccoli and bell pepper; cook for 3–4 minutes, stirring frequently, until crisp-tender.
Return beef (and any juices) to the skillet. Pour in the soy sauce mixture, then bring to a simmer. Stir the cornstarch slurry once more and pour it into the pan. Cook for 1–2 minutes, stirring constantly, until the sauce thickens and coats everything in a glossy glaze. Ensure beef strips reach an internal temperature of 145°F (63°C) before serving.
Spoon rice into bowls, top with the beef teriyaki and vegetables, and garnish generously with sliced green onions and sesame seeds.