Set a large skillet, saute pan, or Dutch oven over medium-high heat. Add the ground beef and cook until no longer pink, breaking apart and stirring as the meat cooks.
While the beef is cooking, combine the beef broth, oyster sauce, soy sauce, honey, rice vinegar, garlic powder, and red pepper flakes in a bowl or large measuring cup; set aside.
After the beef is cooked, push it to the edges of the pan, add the garlic and ginger in the center, and stir for a minute or two until fragrant. Drain the grease from the pan. Add the sauce and the broccoli to the pan; stir to combine. Bring to a boil then reduce to a simmer. Cook for several minutes (using the cooking time on the package of frozen broccoli as a guide) and stir occasionally until the broccoli is cooked to your desired tenderness.
In a small bowl, use a fork to whisk the cornstarch into the water until dissolved. Slowly pour the cornstarch slurry into the pan while stirring the beef and broccoli. Bring to a boil and cook for a minute or two, stirring occasionally, until the sauce is thickened. Stir in the sesame oil, if using, and serve hot over rice or noodles.
You may use fresh broccoli instead of frozen, or you may substitute other veggies for some/all of the broccoli, such as snow peas, shredded or thinly-sliced carrots, baby corn, or bell peppers. Keep in mind that firmer veggies may require a few extra minutes of simmering to become tender. You can always add a little extra broth if too much sauce is evaporating due to additional cooking time.
If you don't have fresh ginger on hand, 1 teaspoon ground ginger may be substituted for the 1 tablespoon fresh, though the ginger flavor in the final dish won't be as strong.
If you don't use LOW-SODIUM beef broth and soy sauce, you dish may turn out too salty.
I like to use natural oyster sauce with no added MSG, which I can typically find it at my regular grocery store.
Many people ask if this recipe can be made without oyster sauce. The answer is yes, although the final dish may be missing some of its depth of flavor. Some commenters have said the recipe turns out fine leaving out the oyster sauce altogether. Otherwise, possible substitutes for the oyster sauce are as follows. You will want to taste and adjust these ingredients if something still seems to be missing.
Increase the total soy sauce in the recipe to 3 1/2 tablespoons and increase the total honey to 1 1/2 tablespoons. Add a splash of Worcestershire sauce, if you like.
Increase the total soy sauce in the recipe to 3 1/2 tablespoons and add 1 1/2 tablespoons hoisin sauce, if you have it.