In a medium bowl, add all of the sauce ingredients. Whisk together until the sugar is dissolved. Set aside.
MAKE THE BEEF AND BROCCOLI:
In a large skillet over medium-heat, heat 1 tablespoon of oil. Add the broccoli and cook, partially covered, for 4 to 5 minutes, stirring or tossing several times until the broccoli is bright green and crisp-tender. Transfer the broccoli to a plate.
In the same skillet over high heat, heat the remaining 1 tablespoon of olive oil. Add the beef in a single layer and cook for about 2 minutes per side, until just cooked through. Add the sauce and reduce the heat to medium-low. Simmer for 3 to 4 minutes, until the sauce thickens slightly. Add the broccoli and stir to combine. If needed, add 1 to 2 tablespoons of water to thin the sauce. It should easily coat the beef and broccoli.
SERVE:
Serve immediately over rice and top with the sesame seeds.
Notes
For easier slicing, cover and freeze your steak for 30 minutes before cooking.
If you prefer softer broccoli, add 2 tablespoons of water in the first step of making the beef and broccoli before covering with the lid. This will steam the broccoli.
Make ahead: This is a great dish for making ahead or for packing up for work or school lunches because the meat re-heats so nicely in the sauce.