Rinse the jasmine rice under cold water until the water runs clear.
In a medium saucepan, combine the rinsed rice and 3 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to low, cover, and simmer for 15 minutes or until the water is absorbed and rice is tender. Remove from heat and let stand covered for 5 minutes.
While the rice is cooking, prepare the stir fry sauce by whisking together soy sauce, oyster sauce, brown sugar, cornstarch, and 1/4 cup water in a small bowl. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced beef and stir fry for 2-3 minutes until browned but not fully cooked. Remove beef from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add broccoli florets and stir fry for 3-4 minutes until bright green and slightly tender.
Add the minced garlic and ginger to the broccoli and stir fry for 30 seconds until fragrant.
Return the beef to the skillet with the broccoli. Stir the prepared sauce again and pour it over the beef and broccoli mixture.
Cook, stirring constantly, for 2-3 minutes until the sauce thickens and the beef is cooked through.
Remove from heat and stir in the sesame oil.
Fluff the cooked rice with a fork and divide it among four plates.
Spoon the beef and broccoli stir fry over the rice and garnish with sliced green onions.