In a small bowl, whisk the soy sauce, cornstarch, honey, rice vinegar, sesame oil, and 1/4 cup water until smooth; set the sauce aside.
Heat 1 tbsp vegetable oil in a large skillet or wok over medium-high. Add the broccoli and stir-fry 3 to 4 minutes, until bright green and crisp-tender. Transfer to a plate.
Add the remaining 1 tbsp oil, then the garlic and ginger; stir 20 to 30 seconds, until fragrant.
Add the beef in a single layer and cook 2 minutes without stirring, then toss and cook 2 to 3 minutes more, until just browned.
Return the broccoli to the pan, pour in the sauce, and cook 1 to 2 minutes, tossing, until the sauce thickens and coats everything.
Serve immediately over jasmine rice.