Bring a large pot of salted water to a boil.
Meanwhile, heat 30 mL (2 tablespoons) of olive oil in a Dutch oven or deep 30 cm (12-inch) skillet over medium-high heat (about 190°C to 205°C) until shimmering.
Add the leeks, season with salt, and cook, stirring often, until softened, which takes about 5 minutes. If the leeks look dry at any point, add a drizzle of olive oil.
Add the mushrooms to the leeks, season lightly with salt, and cook, stirring every 2 minutes, until the mushrooms have browned, about 10 minutes. (If the mushrooms are done before the pasta, adjust the heat to low) .
When the water is ready, add the pasta and cook until al dente.
Halfway through the cooking process, reserve 240 mL (1 cup) of the pasta water and let it cool slightly on the counter.
Drain the pasta in a colander and drizzle with olive oil if it is done before the mushrooms.
When both the mushrooms and pasta are done, stir the miso into the reserved pasta water until it is mostly dissolved.
Add the miso mixture to the Dutch oven or skillet over medium-high heat (about 190°C to 205°C) along with the pasta, cheese, and vinegar. Stir vigorously for 1 to 2 minutes until a cheesy sauce forms and coats the noodles.
Remove the pan from the heat and season to taste with more vinegar if needed.
Garnish with the parsley and more cheese; serve with a final drizzle of oil.
