In a large skillet, heat the vegetable oil over medium 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 and ground ginger to the skillet, stirring for about 1 minute until fragrant.
In a small bowl, whisk together the honey, soy sauce, and cornstarch until smooth. Pour this mixture into the skillet with the beef.
Add the broccoli florets to the skillet, stirring to combine. Cover and cook for 5-7 minutes, or until the broccoli is tender and bright green.
Season with salt and pepper to taste. Serve over cooked rice if desired.