Miso-Cured Black Cod with Chilled Cucumbers

Slice cod 3/4" thick, leaving skin on and bones in (the bones will slip right out when fish is cooked). Season very lightly with salt and place on a paper towel.lined baking sheet. Cover with another paper towel and chill 1 hour (this will draw out some moisture and any fishy flavors).

Combine miso and mirin in a small bowl. Wet 2 paper towels (you can also use cheesecloth) with sake and squeeze out any excess. Spread half of miso mixture in a 13x9" baking dish in a thin, even layer. Cover with a sake-moistened paper towel. Arrange cod in a single layer on top. Cover with the other sakemoistened towel. Spread remaining miso mixture over towel. Cover; chill 3 days.

Preheat broiler. Transfer cod to a rimmed baking sheet; discard miso mixture and paper towels. Broil cod until golden brown around the edges and cooked through, about 4 minutes. Let cool slightly, then pull out bones.

Soak kombu in 2 cups cold water in a small saucepan at room temperature 2 hours, or chill up to 12 hours.

Bring to a bare simmer over medium heat. Discard kombu and bring liquid to a boil. Add katsuobushi; simmer 1 minute (reduce heat if needed). Strain through a paper towel or cheesecloth-lined sieve into a small bowl; discard solids. Let dashi cool.

Bring vinegar, sugar, and 2 tablespoons water to a boil in a clean small saucepan. Remove from heat and stir to dissolve sugar. Let sweet vinegar cool.

Slice cucumbers in half lengthwise. If using Japanese cucumbers, scrape out seeds with a small spoon. Slice cucumbers into very thin half moons. Toss in a small bowl with a few pinches of salt. Let sit until salt begins to draw out water from cucumbers, about 5 minutes. Massage cucumbers, gently at first to keep them from breaking, then more vigorously as they start to expel water, until swimming in water. Rinse in several changes of water; squeeze out excess liquid. Place cucumbers in a clean small bowl and chill until cold, about 1 hour.

After cucumbers have chilled 30 minutes, place ginger and 1 cup water in a small bowl; soak 30 minutes to soften its pungency. Drain.

Add sweet vinegar and 3/4 cup dashi to cucumbers (reserve remaining dashi for another use). Season with salt. Divide cod among shallow bowls. Top with cucumbers and ginger. Pour any cucumber liquid over.

Dashi and sweet vinegar can be made 1 day ahead; cover and chill separately. Chilled cucumbers can be made 1 day ahead; keep chilled.