Prepare marinade by combining sugar, miso, sake and miron in a saucepan. Whisk to blend. Bring to a boil over high heat, then decrease the heat and low and simmer for 45 minutes, stirring occasionally. Remove from heat, transfer to a shallow dish and let cool completely. Add the butterfish and refrigerate overnight.
Prepare sauce by stirring lemon juice into the beurre blanc. Toss in parsley to taste. Set aside and keep warm. To prepare soy drizzle, combine soy sauce and sugar in a small saucepan. Stir over low heat until sugar dissolves. Continue to cook for about 15 minutes or until reduced to 1 cup.
Heat a dry, heavy steel saute pan or skillet over medium heat for 2 to 3 minutes. Remove the fish from the marinade and sear for 3 to 4 minutes on each side, until opaque throughout. Transfer to warmed plates and pour the sauce around the fish. Spoon the soy drizzle over the sauce and serve with rice.