In a medium bowl, combine the soy sauce, brown sugar, sesame oil, minced garlic, grated ginger, and crushed red pepper flakes. Stir until the sugar dissolves to create the sauce.
Heat the vegetable oil in a large skillet over medium-high heat.
Add the lean ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 6-8 minutes.
Drain any excess fat from the skillet.
Pour the prepared sauce over the cooked beef and stir well to coat. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Add the julienned carrot and shredded cabbage to the skillet and stir to combine. Cook for 2 minutes until the vegetables are slightly tender but still crisp.
Divide the cooked white rice evenly among four bowls.
Top each bowl of rice with the Korean beef and vegetable mixture.
Garnish each bowl with sliced green onions and toasted sesame seeds before serving.