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Heat 2 Tbsp. oil in a large skillet over medium-
high heat. Add asparagus, season with salt and
pepper, and cook, stirring occasionally, until
just tender, about 4 minutes. Transfer to a plate.
Heat butter and remaining 1 Tbsp. oil in same
skillet over medium-high heat. Add mushrooms,
season with salt and pepper, and cook, tossing
often, until tender, about 5 minutes. Add shallot
and cook, tossing occasionally, until softened,
about 2 minutes. Toss in oregano, thyme, and
asparagus.
Meanwhile, cook pasta in a large pot of boiling
salted water, stirring occasionally, until al
dente. Drain, reserving 1 cup pasta cooking
liquid.
Add pasta, ½ cup pasta cooking liquid, and 3 oz.
Parmesan to skillet. Cook, tossing and adding more
pasta cooking liquid as needed, until sauce coats
pasta, about 2 minutes; season with salt and
pepper.
Divide pasta among plates and top each with yolks
and more Parmesan.
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