Preheat oven to 350 degrees Fahrenheit.
Spread walnut halves on a rimmed baking sheet; toast until fragrant, 10 minutes. Meanwhile, cook linguine in a pot of boiling salted water until al dente, according to package instructions. Drain; return to pot.
Process half of walnuts, cream, and garlic in a food processor until smooth; season with salt and pepper. Toss with pasta, remaining walnuts, Parmesan, and parsley. Serve with more Parmesan.