In a bowl, whisk together soy sauce, brown sugar, sesame oil, minced garlic, grated ginger, rice vinegar, and gochujang. Place the flank steak in a resealable plastic bag or shallow dish and pour the marinade over it. Seal or cover and marinate in the refrigerator for at least 30 minutes, or up to 4 hours for more flavor.
While the steak is marinating, prepare the spicy cream sauce by mixing sour cream, mayonnaise, lime juice, and sriracha in a small bowl. Adjust the sriracha to your desired spice level. Set aside.
Preheat a grill or grill pan over medium-high heat. Remove the steak from the marinade and discard the marinade. Grill the steak for about 4-5 minutes per side for medium-rare, or until desired doneness. Let the steak rest for 5 minutes before slicing it thinly against the grain.
To assemble the bowls, divide the cooked rice among four bowls. Top each bowl with sliced steak, shredded carrots, cucumber slices, and sliced green onions.
Drizzle the spicy cream sauce over the top and sprinkle with sesame seeds for garnish. Serve immediately.