Peel and wash burdock and carrots. Cut them into 1-inch length & ¼ inch wide. I like mine diagonal but julianne works well.
Place a medium frying pan on a stove top and turn the heat to medium. Add 1 teaspoon of sesame oil then burdock and carrots. Sautee for about a minutes.
Add brown sugar then dashi to the frying pan. Stir well then turn the heat to medium high. Add soy sauce and cook continuously for about 10 minutes. Stir occasionally.
Add 3 tablespoon of mirin and continue cooking until liquid is almost all gone, about 5 minutes. Taste test.
Turn heat off then add 1 teaspoon of sesame oil. Sprinkle sesame seeds.