Slice the beef into thin slices against the grain.
Mix together the sliced beef, rice wine, cornstarch, shoyu, and garlic in a small bowl.
Add cooking oil to a large pan and adjust the stove to high heat. Add in the beef mixture when the pan is hot and stir.
As soon as the color begins to change, remove from pan and put the beef back into the small bowl. Leave on the side for later.
With the pan still on high heat, add in the broccoli. There should still be some oil left in the pan bubbling (which is why we started with more oil than usual). While the broccoli cooks, add salt, pepper, shoyu, water, and brown sugar. Cover and cook for 1 - 2 minutes. In the meantime, prepare the thickening agent.
Uncover and add the cooked beef back in. Mix.
Add in the thickening agent and mix. Turn off the stove and add sesame seed oil.