Step 1

Cook pasta in a large pot of boiling generously salted water, stirring occasionally and adding asparagus when pasta has 1 minute left to go, until pasta is very al dente, about 3 minutes less than package directions.

Step 2

Meanwhile, combine garlic and oil in a medium Dutch oven or other high-sided pot and set over medium heat; season very generously with pepper. Cook, stirring often, until garlic is light golden, about 2 minutes. Remove from heat and stir in paprika; set aside.

Step 3

Place egg yolks in a medium bowl. Scoop out 1 cup cooking liquid from pasta and, whisking constantly, gradually add to egg yolks to temper. Season with salt and pepper; set aside.

Step 4

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.

Step 5

Divide pasta among shallow bowls and top with more Parmesan and a few grinds of pepper.