Cook the jasmine rice according to package directions in a separate saucepan and set it aside.
Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Add the sliced flank steak and cook for 2 to 3 minutes until it is no longer pink. Remove the beef from the skillet and set it aside.
Add the remaining tablespoon of vegetable oil to the same skillet. Stir in the minced garlic and grated ginger, then cook for 30 seconds until fragrant. Add the broccoli florets and cook for 3 minutes, stirring often.
Return the beef to the skillet. Stir together the soy sauce, beef broth, cornstarch, and sesame oil in a small bowl, then pour the mixture over the beef and broccoli. Cook for another 2 minutes, stirring until the sauce thickens and coats everything evenly.
Spoon the cooked jasmine rice into bowls and top with the beef and broccoli stir-fry.