Julienne the carrots by halving them crosswise, slicing thinly on a diagonal, then stacking and cutting into thin strips. Alternatively, grate the carrots using a box grater or use pre-julienned carrots from the grocery store.
Heat the sesame oil in a large skillet over medium heat. Add the carrots to the pan and stir-fry until the carrots are cooked through, about 3 minutes. If the pan is dry, add water, a couple of tablespoons at a time.
Add the soy sauce, mirin, and red pepper flakes (if using) and continue to stir-fry until most of the liquid has cooked off and the carrots are coated with the sauce, about 2 minutes. Serve.
