Toast the walnuts in a large skillet over medium heat until they smell nutty and turn golden, about 2 to 4 minutes—stay close and toss them frequently to prevent scorching. Process one cup of the toasted nuts in a food processor until finely ground, then pulse the remaining half-cup until coarsely chopped to ensure the sauce has both body and texture.

Simmer the wine in the same skillet over medium-high heat until it reduces to about a quarter-cup, about 3 minutes. Whisk in the cream, all the walnuts, Parmesan, salt, and pepper, then remove the pan from the heat and cover it to keep the sauce from cooling or skinning.

Boil the pasta in salted water in a large Dutch oven until it is tender but still al dente, about 2 to 3 minutes. Reserve a cup of the starchy cooking water before draining; this liquid is the secret to a smooth, cohesive sauce.

Combine the pasta and a half-cup of the cooking water with the sauce in the skillet over medium heat, tossing constantly until the sauce is hot and clings to the pasta. Add more cooking water as needed to reach a glossy consistency, then stir in the chives and serve immediately while the sauce is silky.