Make pesto by adding basil, garlic, pine nuts, Parmesan cheese and salt into the bowl of a food processor. Pulse until finely chopped; scrape down sides. With food processor running, add olive oil through the shoot in a steady stream; process until smooth. Transfer pesto to a medium bowl and stir in heavy cream; taste and season with more salt if needed. (recipe note #1)
For the Pasta
Cook pasta until firm to the bite (al dente) according to package directions, in a large pot of boiling, salted water. Drain, reserving 1 cup of pasta water. (recipe note #2)
For the Chicken
Meanwhile, in a large skillet, heat the olive oil over medium heat until it starts to shimmer. Add chicken and season with salt and pepper; cook and stir until chicken is just cooked through, about 4 minutes. Add pesto mixture; cook and stir until bubbly, about 2 minutes.
Add drained pasta to chicken and pesto mixture and stir until well combined and heated through, adding pasta water a tablespoon at a time if needed to loosen the sauce; season to taste with salt and pepper. Transfer to serving bowl or platter and sprinkle with more parmesan cheese and chopped basil if desired; serve.
Video
Notes
Transfer pesto to bowl and refrigerate if making more than a few minutes in advance. Cover with plastic wrap touching the surface to preserve the vibrant green color.
If you have leftover pasta, cover and refrigerate the reserved pasta water as well for an excellent way to moisten pasta when reheating.