In a medium bowl, whisk together soy sauce, gochujang, brown sugar, sesame oil, rice vinegar, ginger, garlic, and black pepper. Add chicken and toss to coat. Marinate for at least 15 minutes (longer is better!).
In a small bowl, whisk together cornstarch and water until smooth. Set aside.
Heat a large skillet or wok over medium-high heat. Add marinated chicken and cook, stirring occasionally, until browned and cooked through (about 8-10 minutes).
Stir in the cornstarch slurry and cook for 1-2 minutes, or until the sauce has thickened slightly.
While the chicken is cooking, prepare the gochujang cream sauce. In a small bowl, whisk together mayonnaise, gochujang, milk, rice vinegar, and sesame oil until smooth and creamy.
To assemble the bowls, divide cooked rice between bowls. Top with the Korean BBQ chicken, shredded carrots, shredded red cabbage, and green onions.
Drizzle generously with the gochujang cream sauce.