In a large skillet, heat the vegetable oil over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain excess fat if necessary.
Add the minced garlic to the skillet and sauté for 1-2 minutes until fragrant.
Stir in the broccoli florets and cook for another 3-4 minutes until they are bright green and tender-crisp.
In a small bowl, whisk together the honey, soy sauce, cornstarch, and water until smooth. Pour this mixture over the beef and broccoli in the skillet.
Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens. If desired, drizzle with sesame oil and season with salt and pepper to taste.
Serve the honey garlic ground beef and broccoli over cooked rice.