Heat a large skillet or wok over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a wooden spoon, about 5-7 minutes. Drain excess fat if needed.
Add the diced onion and minced garlic to the skillet. Sauté for 2-3 minutes until the onion is translucent.
Stir in the sliced cabbage and cook for another 5 minutes, stirring frequently, until the cabbage is tender.
In a small bowl, mix together the soy sauce, brown sugar, sesame oil, ground ginger, and red pepper flakes (if using). Pour this mixture over the beef and cabbage, stirring well to combine.
Cook for an additional 2-3 minutes, allowing the flavors to meld together. Remove from heat.
Serve hot, garnished with chopped green onions.