Cook pasta according to package instructions.
While pasta cooks, heat heavy whipping cream and lemon zest over medium heat in a small pot, stirring occasionally.
Toast pistachios on a baking sheet for 2-3 minutes, if desired.
Add parsley, parmesan, pistachios, garlic, lemon juice and pistachios in a food processor or blender. Pulse until combined.
While the food processor or blender is running, add olive oil. Blend until smooth.
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.
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.