Mix brown sugar, soy sauce, cornstarch and lemon juice in a bowl. Stir to break up lumps of starch. Transfer the sliced beef to a bowl and stir to combine. Leave for 15 minutes.
Put the broccoli florets in a hot frying pan greased with frying oil. Fry for 5-6 minutes, stirring with a spatula. Then transfer to a plate and set aside.
Mix all the ingredients for the sauce in a deep bowl. Whisk with a whisk to combine well.
Add frying oil to a hot pan and fry the beef for 5-6 minutes, stirring occasionally. Make medium heat. During this time, the beef should have time to cook, as it was thinly sliced and marinated. If you use beef for a long stew, then after frying it will remain tough. Transfer the fried beef to a plate and set aside.
Pour the sauce into the pan and heat for 3-4 minutes, stirring, until it becomes thick and glossy.
Transfer the beef to the pan and fry in the sauce for another 3 minutes.
Add broccoli and fry everything together for another 2-3 minutes.
Serve beef and broccoli hot or warm, sprinkled with sesame seeds.