Step 1

Stir together 4 cups filtered water, kombu, and shiitakes in a medium bowl. Let stand at room temperature at least 8 hours or up to overnight. Remove kombu and mushrooms; discard or, if desired, reserve to make another batch of dashi.

Step 2

Sprinkle duck breasts all over with salt. Place duck, skin side up, on a plate. Refrigerate, uncovered, at least 8 hours or up to overnight.

Step 3

Combine soy sauce, hon mirin, and sugar in a large saucepan. Cook over medium, stirring occasionally, until mixture just begins to simmer and sugar is dissolved, 3 to 4 minutes. Stir in dashi, leek strips, and, if using, sake. Bring to a boil over medium-high. Reduce heat to medium-low; simmer, stirring occasionally, until leek is tender and mixture has reduced to about 4 cups, 20 to 25 minutes. Cover dipping sauce, and keep warm over low until ready to serve.

Step 4

Heat a medium skillet over medium. Place duck breasts, skin sides down, in skillet; reduce heat to medium-low. Cook, undisturbed, occasionally spooning off drippings from skillet, until fat is rendered and skin is golden brown, 10 to 12 minutes. Flip duck breasts; cook until a thermometer inserted in thickest portion registers 130°F for medium-rare, 2 to 4 minutes. Transfer duck to a cutting board; let rest 10 minutes.

Step 5

To serve, divide dipping sauce evenly among 4 bowls. Cut duck breasts crosswise into 1/4-inch-thick slices, and add to bowls. Top evenly with citrus peel and ginger strips; garnish with mitsuba, togarashi, and serrano. Serve immediately with cold soba noodles.