In a large skillet or wok, 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.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
In a small bowl, whisk together the soy sauce, brown sugar, sesame oil, ginger, and red pepper flakes (if using). Pour this mixture over the cooked beef and stir well to combine.
Add the broccoli and bell peppers to the skillet. Cook for 4-5 minutes, stirring occasionally, until the vegetables are tender-crisp.
Stir in the chopped green onions and cook for another minute.
Serve the Korean beef stir-fry over cooked rice and sprinkle with sesame seeds.