How to Make It
Peel stems of mushrooms, if woody; separate stems from caps. Reserve 4 of the firmest caps. Slice remaining mushroom caps into 1/4-inch slices, no more than 2 inches long. Finely chop mushrooms stems, and set aside.
Heat 3 tablespoons oil in a large skillet over medium. Add onions and thyme; cook, stirring occasionally, until onions are tender and translucent, about 8 minutes. Add remaining 2 tablespoons oil, and increase heat to high. Add sliced mushroom caps and chopped stems, and cook, undisturbed, 4 minutes. Stir in garlic and 2 teaspoons salt. Cook, stirring occasionally, 3 minutes. Add wine, and cook, undisturbed, until liquid is reduced by half, about 3 minutes. Remove from heat, and stir in crushed red pepper and black pepper. Remove and discard thyme sprigs.
Meanwhile, shave reserved 4 mushroom caps on a mandoline or slice very finely with a sharp knife. Set aside.
Bring 6 quarts water to a boil in a large pot over high. Add 1/4 cup salt, and stir to dissolve. Add pasta, and cook until al dente, 4 to 6 minutes. Reserve 2 cups cooking liquid; drain pasta.
Return pot to medium heat; add mushroom mixture and 13/4 cups cooking liquid. Bring to a simmer. Add cooked pasta. Cook, stirring gently with tongs, until sauce thickens slightly, 1 to 2 minutes. Add butter, and cook, stirring constantly, until a creamy sauce forms and coats pasta, about 2 minutes, adding additional 1/4 cup cooking liquid if needed. Remove from heat, and stir in cheese, nepitella, and remaining 1 teaspoon salt. Transfer pasta to a serving dish, and garnish with shaved mushroom caps. Serve hot.