In a small mixing bowl, whisk together the beef broth, soy sauce, brown sugar, and sesame oil until the sugar is dissolved.
In a separate small container, mix the cornstarch and 2 tablespoons of water to create a slurry and set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add the broccoli florets and 2 tablespoons of water to the skillet; cover with a lid and steam for 3 minutes until tender-crisp.
Remove the broccoli from the pan and set aside on a plate.
Add the ground beef to the same skillet and cook, breaking it into crumbles with a spatula, until browned and no longer pink.
Drain any excess fat from the pan.
Add the minced garlic and grated ginger to the beef and cook for 1 minute until fragrant.
Pour the prepared sauce mixture into the skillet with the beef and bring to a light simmer.
Stir in the cornstarch slurry and continue to cook for 1 to 2 minutes until the sauce has thickened and is glossy.
Return the cooked broccoli to the skillet and toss everything together until evenly coated in the sauce.
Serve immediately over steamed rice or noodles.