Prepare the gobo. Wash and pat dry. Use a knife to gently remove the thin outer skin layer (don't use a vegetable peeler because that will remove too much of the gobo).
Cut the gobo into thin slices on the diagonal. Then cut each slice into thin strips. Soak the gobo strips in a large bowl of water for 10 minutes. This will help keep the gobo from browning too quickly.
While the gobo is soaking, peel and cut the carrot into thin strips. Aim to get the carrots the same size as the gobo. Set aside.
Drain the gobo, then give it a gentle rinse under water. Drain again.
Add the sesame oil to a large pan over medium heat. Then add the gobo and saute for 3 minutes.
Mix the dashi powder with ½ cup of water in a small bowl. Pour it over the gobo and let cook on low heat for 5 minutes (add more water if needed). This step is to help soften the gobo.
Bring the heat back up to medium, then add the carrots and saute for another 5 minutes. Season with the mirin and soy sauce.
Saute for 2-3 minutes until everything is well mixed and the gobo and carrots are nice and tender. Add the sesame seeds, give it a good mix, and the dish is ready to eat!
Best hot and fresh, with a good bowl of rice ^_^