Wash and peel fresh lotus root and slice thinly, then quarter the rounds. Soak in 2 cups of water for 5-10 minutes. Soak arame in 2 cups water for 5-10 minutes.
Heat oil over medium heat in a skillet. Drain the lotus root, and saute for 2-3 minutes. Remove arame from the soaking water by lifting it out carefully (do not tip water off). Add arame to the skillet, toss with the lotus root and cook a further 3 minutes. Add arame to the skillet, toss with the lotus root and cook a further 3 minutes. Add arame soaking water to nearly cover the arame. Bring to a boil and then turn down heat and simmer covered for 15 minutes.
Cut the carrot into thin julienne strips and place on top of the arame. Simmer for 5 minutes. Add the mirin and the 2 teaspoons of shoyu and gently stir through. Remove cover and allow excess water to evaporate. Serve with a garnish of parsley.