Mix soy sauce, brown sugar, sesame oil, garlic, ginger, rice vinegar, and gochujang in a bowl. Add steak slices and coat well. Refrigerate for at least 30 minutes so flavors soak into the meat.
Rinse rice until water runs clear for fluffier texture. Cook with water and salt until tender and keep warm. Preparing rice while the steak marinates saves time.
Whisk mayonnaise, Sriracha, lime juice, and honey until smooth. Taste and adjust spice or sweetness as needed. Refrigerate until ready to serve.
Heat a skillet over medium-high heat and cook marinated steak for 3–4 minutes per side until nicely browned. Let meat rest briefly, then slice thinly for tender bites.
Add rice to serving bowls, top with steak, carrots, cucumbers, and optional kimchi. Finish with spicy cream sauce, green onions, and sesame seeds for color and flavor.