Scrub the gobo skin well or peel the skin. Cut into matchsticks and soak in a bowl of water while you prepare the carrots.
Peel carrots and cut into matchsticks; make sure they are similar in size to the gobo.
Mix together soy sauce, sake, mirin, and sugar in a small bowl.
Drain the gobo, getting rid of as much water as you can (water will splash when it hits the oil). Heat a fry pan over medium heat with the sesame oil, and once fragrant add the gobo and red pepper flakes. Stir to coat the gobo with oil and cook for 1 minute.
Add carrots, cook for 1 minute, then add in the soy sauce mixture and continue cooking until the liquid is gone. Turn off the heat and sprinkle with sesame seeds.