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, then reduce heat to low, cover, and simmer for 15 minutes or until water is absorbed and rice is tender. Remove from heat and let stand covered for 5 minutes.
In a small bowl, whisk together soy sauce, oyster sauce, cornstarch, and beef broth until smooth. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the thinly sliced flank steak to the skillet. Season with salt and black pepper. Stir-fry for 3-4 minutes until browned but not fully cooked through. Remove the beef from the skillet and set aside.
In the same skillet, add the broccoli florets and 2 tablespoons of water. Cover and steam for 3 minutes until broccoli is bright green and slightly tender. Remove the broccoli and set aside with the beef.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add minced garlic, minced ginger, diced carrots, and peas. Stir-fry for 2 minutes until fragrant and vegetables begin to soften.
Push the vegetables to one side of the skillet and pour the beaten eggs into the empty side. Scramble the eggs until just set, then mix with the vegetables.
Add the cooked rice to the skillet and stir to combine with the vegetables and eggs. Cook for 2-3 minutes, stirring frequently, to heat through.
Return the beef and broccoli to the skillet. Pour the prepared sauce over the mixture. Stir well to coat all ingredients. Cook for an additional 2-3 minutes until the sauce thickens and the beef is cooked through.
Drizzle the sesame oil over the stir fry and toss to combine.
Remove from heat and garnish with sliced green onions before serving.