Whisk together soy sauce, sesame oil, brown sugar, garlic, ginger, rice vinegar, and black pepper in a bowl.
Add sliced steak and toss to coat. Let marinate at room temperature for 15 to 30 minutes.
Heat a large skillet or grill pan over medium-high heat.
Cook the marinated steak in a single layer for 2 to 3 minutes per side until browned and cooked through. Remove from heat.
In a small bowl, whisk mayonnaise, gochujang, sriracha, honey, and rice vinegar. Add water if a thinner sauce is desired.
Divide cooked rice among four bowls.
Top each bowl with cooked steak, shredded carrots, cucumbers, and cabbage or lettuce.
Drizzle spicy cream sauce over the bowls.
Garnish with sliced green onions and sesame seeds before serving.