In a large bowl, whisk together soy sauce, brown sugar, sesame oil, minced garlic, grated ginger, rice vinegar, and gochujang (if using). Add the flank or sirloin steak and marinate for at least 30 minutes.

In a small bowl, combine the mayonnaise, sriracha, lime juice, and honey to make the spicy cream sauce. Whisk until smooth and set aside.

Heat a skillet over medium-high heat. Cook the marinated steak slices for 2-3 minutes per side until caramelized and slightly charred.

In a bowl, layer cooked rice at the base and top with the sliced steak, shredded carrots, thin cucumber slices, and kimchi if using.

Drizzle the spicy cream sauce generously over the topped bowls.

Garnish with sliced green onions and sesame seeds, then serve immediately.