In a mixing bowl, whisk together soy sauce, sesame oil, brown sugar, minced garlic, and grated ginger until fully combined. Place the boneless, skinless chicken thighs in the marinade and let them marinate in the refrigerator for at least 20 minutes.

While the chicken marinates, prepare the creamy sauce. In a separate bowl, mix gochujang, sour cream, honey, and lime juice until smooth. Season with salt and pepper to taste, then set aside.

Heat a grill pan or skillet over medium-high heat for about 5 minutes. Add the marinated chicken thighs and cook for 6-7 minutes on each side until caramelized and cooked through.

Distribute cooked jasmine rice into individual bowls as a base. Slice the grilled chicken and lay it over the rice. Add shredded carrots, chopped cucumbers, and shredded red cabbage.

Drizzle each bowl with the gochujang cream sauce. Sprinkle with sliced green onions and sesame seeds, and serve with lime wedges on the side.