How to Make It
Place flour and 1 tablespoon salt in a food processor; pulse until combined. Beat egg yolks, whole egg, and 1 1/2 tablespoons oil in a medium bowl. Add egg mixture to food processor, and pulse until dough just comes together. Gradually add water, 1 tablespoon at a time, if dough is too dry or doesn’t come together. Transfer dough to a lightly floured work surface, and knead until very smooth, 5 to 10 minutes. Cover dough with plastic wrap, and let stand at room temperature for 1 hour.
Pinch off a 1/2-inch piece of dough, and roll it between your hands to form a thin 2- to 3-inch-long rope; transfer to a rimmed baking sheet. Repeat with remaining dough.
Bring a large saucepan of salted water to a boil. Cook pasta until al dente, about 7 minutes. Drain, reserving 1/2 cup cooking liquid. Toss pasta with 1 teaspoon oil in a bowl to prevent sticking. Wipe out saucepan with paper towels.
Add remaining 1/4 cup oil to saucepan, and heat over medium-high. Add mushrooms to pan, and season to taste with salt and black pepper. Cook, stirring occasionally, until tender and lightly browned, about 8 minutes. Add asparagus and crushed red pepper, and cook, stirring, until crisp-tender, 2 to 3 minutes. Add wine, and cook, scraping up any browned bits from the pan, until liquid is absorbed, about 2 minutes.
Add pasta, heavy cream, lemon juice, and reserved 1/2 cup cooking liquid to pan. Reduce heat to medium, and cook, tossing, until pasta is lightly coated, about 2 minutes. Season to taste with salt and black pepper. Transfer to 6 shallow bowls, and serve immediately with shaved ricotta salata.