Combine all the ingredients for the sauce in a small bowl and set aside.
Season the beef with salt and pepper.
Heat 1 Tbsp oil in a large enough pan, add broccoli florets and 1/4 cup water to the pan. Cover and let simmer, for 2–3 minutes, until the water has evaporated, and the broccoli is almost tender and bright green. Remove the broccoli from the pan and set aside.
Add 1 Tbsp oil to the pan and spread out steak pieces in it. Fry for 2 minutes, then flip and fry for another minute. Add minced garlic and ginger, cook 30 seconds more.
Pour in the sauce and toss to coat, bring to a simmer and cook for 2 minutes.
Remove from heat, stir in the cornstarch slurry, put back on heat and bring to a simmer. Add the broccoli back in and stir until the sauce has thickened.
Serve over rice, sprinkled with sesame seeds.