Drain pasta and asparagus, reserving 2 cups pasta cooking liquid; transfer pasta and asparagus to pot with reserved garlic oil. Set back over medium heat and toss to coat. Tossing constantly, add 1 cup pasta cooking liquid, followed by reserved yolk mixture, then ¾ cup Parmesan. Cook, tossing constantly and reducing heat as needed to keep mixture below a simmer, until cheese is melted and liquid thickens enough to coat pasta in a glossy, silky sauce, about 5 minutes. (This might be easier on your hands if you use 2 wooden spoons, as though you were tossing a salad, rather than trying to do it with 1 hand and a pair of tongs.) Add more reserved pasta cooking liquid if needed to loosen.
Source: Thanks https://www.bonappetit.com/recipe/vegetarian-carbonara