Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente, adding the spinach during the last 30 seconds of cooking. Reserve 1 cup cooking water, then drain the pasta and spinach.
Meanwhile, melt the butter in a large skillet over medium heat. Add the heavy cream, nutmeg, lemon zest and 1/2 teaspoon salt. Increase the heat to medium high and bring the liquid to a simmer. Add the pasta and spinach and toss until coated, about 1 minute. Stir in the cheese and season with salt and pepper. Stir in enough of the reserved cooking water to loosen the sauce.
Remove from the heat and immediately stir in the pesto. Divide among bowls; top with pepper and more parmesan.