In a small bowl, whisk together the soy sauce, honey or brown sugar, rice vinegar, toasted sesame oil, minced garlic, minced ginger, and crushed red pepper. Set aside.
In a large skillet or pan over medium-high heat, brown the ground beef, breaking it apart as it cooks. Once the beef is fully browned, drain off any excess fat if needed.
Pour the sauce mixture into the skillet, stirring well to ensure the beef is coated. Let it simmer for a few minutes until the sauce is slightly reduced and beef is fully flavored.
To serve, scoop rice into each serving bowl. Top with the Korean beef mixture. Garnish with shredded carrot, sliced green onions, sliced cucumber, and a sprinkle of sesame seeds.