Toast the walnuts in a dry skillet over medium heat for 2-3 minutes, or until fragrant. Let them cool completely.
Place the toasted walnuts, fresh basil, grated Parmesan cheese, and minced garlic in a food processor. Add the olive oil and blend until smooth.
In a saucepan, gently heat the heavy cream over low heat, being careful not to let it boil.
Add the walnut pesto to the cream and stir well to combine. Cook for 2-3 minutes to allow the flavors to meld.
Season with salt and freshly ground black pepper, then mix thoroughly.
Serve warm with pasta, grilled meats, or vegetables, and sprinkle with additional grated Parmesan cheese.
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