Misoyaki

Make marinade: Whisk together miso, sugar, sake, and mirin in a saucepan; bring to a boil. Reduce heat to low and simmer, stirring occasionally, until marinade has reduced, about 45 minutes. Transfer marinade to a shallow dish and cool completely, 30 minutes to 1 hour. Place butterfish in marinade and refrigerate, 8 hours to overnight.

Make beurre blanc: Combine vinegar, wine, shallot, bay leaf, and peppercorns in a saucepan; bring to a boil. Reduce heat to medium and simmer until only about 1 tablespoon liquid remain, 2 to 3 minutes. Pour in cream and simmer until mixture is reduced by half, 2 to 3 minutes. Increase heat to medium-high and rapidly whisk in butter pieces, one at a time, until beurre blanc is smooth and thickened. Strain beurre blanc through a mesh strainer to remove spices.

Make lemon sauce: Stir lemon juice into beurre blanc until lemon sauce is evenly mixed; fold in parsley.