In a small bowl, combine egg white, flour, a pinch of salt, and about 1/4 tsp freshly ground black pepper. Mix together to form a smooth dough, adding water, a teaspoon at a time, if necessary. Knead for 5 minutes. Wrap in plastic and let rest 30 minutes.

Roll and cut dough to form spaghetti. Set aside.

Heat oil in a small skillet over medium-high heat. Add mushrooms and sear for 3 minutes. Stir to flip and sear the other side. Transfer to a large serving bowl. When cool, top with cheese and egg yolk.

Bring a medium saucepan of salted water to a boil. Add spaghetti and cook until al dente. Reserve 1/2 cup pasta water before draining thoroughly.

Add hot pasta to bowl and immediately begin tossing to incorporate mushrooms, cheese, and egg yolk. If needed, add hot pasta water to make a creamy sauce.

Serve with a generous grind of pepper.