In a bowl, whisk together the soy sauce, brown sugar, sesame oil, garlic, ginger, rice vinegar, and gochujang until well combined.
Place the flank steak in a resealable plastic bag or shallow dish and pour the marinade over it. Seal the bag or cover the dish and marinate in the refrigerator for at least 30 minutes, or up to 4 hours for more flavor.
Preheat a grill or skillet over medium-high heat. Remove the steak from the marinade and discard the marinade.
Season the steak with salt and pepper. Grill or sear the steak for about 4-5 minutes per side, or until it reaches your desired level of doneness. Let it rest for 5 minutes before slicing thinly against the grain.
To assemble the bowls, divide the cooked jasmine rice among four bowls. Top each bowl with sliced steak, shredded carrots, sliced cucumbers, and green onions. Sprinkle with sesame seeds before serving.