Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1/2 cup of pasta water before draining. Drain and rinse under cold water to stop cooking; set aside.
In a large bowl, whisk together pesto, heavy cream, and lemon juice until smooth and well combined.
Add the cooled pasta to the bowl with the dressing. Toss well until every piece is coated. If the dressing seems too thick, add reserved pasta water one tablespoon at a time until you reach your desired consistency.
Gently fold in the halved cherry tomatoes and spinach. The spinach will wilt slightly from the residual warmth of the pasta.
Stir in the grated Parmesan cheese. Season with salt and pepper to taste.
Garnish with additional Parmesan and optional nuts if using. Serve immediately at room temperature or refrigerate for later.