Bring a large pot of water to a boil.
Whisk egg yolks and eggs in a medium bowl until no streaks remain, whisk in Parmesan; season with pepper.
Heat 2 tablespoons oil in a large Dutch oven or pot over medium-high. Add mushrooms and cook, stirring occasionally, until golden brown, about 10 minutes. Transfer mushrooms to a plate.
Season boiling water with 2 tablespoons kosher salt, add pasta and cook 2 minutes less than package instructions, stirring occasionally. Measure out 1 ¾ cups pasta cooking water. Add 1 cup cooking water and truffle butter to Dutch oven; bring mixture to a boil over medium-high. Drain pasta then transfer to Dutch oven.
Cook pasta, stirring and gently tossing constantly with tongs, until al dente and water is reduced by about half; about 2 minutes. Remove pot from heat.
Whisk ¼ cup reserved pasta cooking water into egg mixture. Slowly stream egg mixture into pasta, stirring and gently tossing constantly with tongs, until cheese is melted and egg is thickened to form a glossy sauce on the pasta.
Thin sauce with remaining ½ cup reserved pasta cooking water, adding a 1–2 tablespoons at a time, until consistency of heavy cream is reached. Season to taste with additional truffle butter and salt.
Mix in mushrooms and divide pasta among serving bowls. Top with thin shavings of truffle, ground pepper and additional parmesan.