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Cook pasta according to package instructions.
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While pasta cooks, heat heavy whipping cream and lemon zest over medium heat in a small pot, stirring occasionally.
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Toast pistachios on a baking sheet for 2-3 minutes, if desired.
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Add parsley, parmesan, pistachios, garlic, lemon juice and pistachios in a food processor or blender. Pulse until combined.
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While the food processor or blender is running, add olive oil. Blend until smooth.
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Place the pesto in a large bowl. Slowly stir in cream and lemon zest mixture until smooth and blended completely. Salt and pepper to taste.
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Drain pasta and add to bowl with pesto sauce. Toss to combine. Serve immediately. Garnish with a sprinkle of parmesan and chopped parsley if desired.