⅓ cup coarsely chopped white or yellow onion
2 Tbsp. coarsely chopped parsley or cilantro stems
2 scallions, whites only, coarsely chopped
1 medium carrot, peels only
1 garlic clove
¾ cup dried rice koji
1 Tbsp. plus 1 tsp. kosher salt
For the mushrooms:
1 Tbsp. olive oil
8 oz. cremini mushrooms, halved
5 Tbsp. unsalted butter
1½ tsp. rice vinegar
Make the koji sauce: To a food processor, add the onion, parsley stems, scallions, carrot peels, and garlic and process into a coarse paste. Scrape into a sterilized 1-quart glass jar, then stir in the koji, salt, and ¾ cup plus 1 tablespoon of water. Cover tightly with the lid and set aside at room temperature (65–70°F) away from direct sunlight.
Once a day, remove the lid and stir the mixture. After 7 days, the smell of the alliums will mellow and the mixture will taste umami and mildly funky. (It will keep covered in the fridge for up to 8 months.)
Make the mushrooms: To a large skillet over medium heat, add the oil. When it’s hot and shimmering, add the mushrooms cut-side down and cook until the bottoms are golden brown, 6–8 minutes. Turn and continue cooking until the other sides are golden brown, 3–4 minutes more. Add the butter and cook, stirring occasionally, until the butter melts and begins to foam, about 1 minute. Stir in 1 tablespoon of the koji sauce and cook, continuously basting the mushrooms with the sauce, until the sauce is glossy and reduced by about half, about 2 minutes. Stir in the rice vinegar, then transfer to a platter and serve warm.