In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the minced garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes. Season with salt and pepper.
While the beef is cooking, in a small bowl, whisk together the honey, soy sauce, cornstarch, and water until smooth.
Once the beef is cooked, add the broccoli florets to the skillet. Stir-fry for about 3-4 minutes until the broccoli is bright green and tender-crisp.
Pour the honey-soy mixture over the beef and broccoli. Stir well to coat everything evenly and cook for an additional 2-3 minutes until the sauce thickens.
Serve the stir-fry over cooked rice or noodles.