Peel burdock root and diagonally slice thinly 2 inch length pieces, stack a few strips and cut into thin matchbox strips. Soak the gobo in water or vinegar water (just one drop of vinegar). Change water a couple of times until the water is clear, and then keep the burdock root in the water until ready to cook.
Cut carrot into matchbox strips.
In a frying pan, heat oil over medium high and stir fry the burdock root and then the carrot after a few minutes.
Add the seasonings and cook until most of the liquid evaporates.
When the liquid is almost gone, add sesame oil and sprinkle sesame seeds and ichimitogarashi.