Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, 7 to 9 minutes or according to package instructions. Reserve 3/4 cup of the cooking water. Drain the pasta and set it aside.

Meanwhile, melt 2 tablespoons of the butter in a large, high-sided skillet over medium heat. Add the shallot and garlic and cook, stirring frequently, until slightly softened, about 3 minutes. Stir in the mushrooms, salt, and pepper. Cook, stirring occasionally, until the mushrooms are browned and tender, about 5 minutes.

Add the remaining 6 tablespoons of butter and stir until melted. Whisk in the miso and reserved pasta water. Simmer until the sauce starts to thicken, 1 to 2 minutes. Add the pasta and toss to coat with the sauce. Remove from the heat and stir in the basil and red pepper flakes.