In a small saucepan, combine the sake, soy sauce, mirin, sugar, ginger, garlic and shiitake mushrooms (if using). Simmer over medium, then reduce to medium-low and cook until slightly thickened, about 15 minutes. Strain through a mesh sieve into a measuring cup or small bowl, pressing the solids; you should have ½ to ⅔ cup tare. Discard the solids or reserve for another use.

Season the chicken on both sides with 1¼ teaspoons each salt and white pepper. Pour ¼ cup of the tare into a 9-by-13-inch baking dish or other wide, shallow container then place the chicken skin side up in a single layer in the tare, allowing the meat to marinate without moistening the skin. Let stand at room temperature at least 15 minutes or up to 1 hour.

Heat the broiler on high with the rack in the lower-middle position. Set a wire rack in a broiler-safe rimmed baking sheet. Remove the chicken from the tare and place the pieces skin side up on the rack. Pat the skin dry without wiping off the seasoning; discard any tare remaining in the baking dish. Broil the chicken until the skin is rendered and golden brown, 15 to 17 minutes.

Remove from the oven. Lightly brush the chicken with some of the remaining tare, then continue to broil until the skin is crisped and caramelized, 4 to 6 minutes. Remove from the oven and let rest for a few minutes.

Transfer the chicken to a cutting board. Using a chef’s knife, cut each thigh crosswise into 3 or 4 pieces. Transfer to a platter and drizzle with additional tare. (Store extra tare in an airtight container in the refrigerator for a few weeks.)

Faux Yuzu Kosho: In a mortar with a pestle, grind 2 tablespoons chopped drained pickled jalapeño chilies (patted dry), 2 tablespoons chopped lemon zest (from about large 4 strips) and 1 teaspoon kosher salt until smooth. Use right away or refrigerate in an airtight container up to 1 week.