How to Make It
Season the chicken breast with 1/8 teaspoon each of sea salt and freshly ground pepper. In a small pan, heat 1 tablespoon of the extra-virgin olive oil over medium high heat. Add the chicken and cook for 1 minute. Turn the chicken, reduce the heat, cover and cook for 8 minutes. Remove the pan from the heat and leave covered for 10 minutes, then shred the chicken with 2 forks.
Meanwhile, in a large pot of boiling salted water, cook the pasta according to package directions.
In a large frying pan, heat the remaining 1/4 cup of extra-virgin olive oil over medium high heat. Add the onion and cook for 5 minutes, or until it just starts to brown. Add the garlic and cook for 30 seconds. Add the mushrooms and cook until they are soft and browned, about 10 minutes. Add the kale and cook for 1 minute, until it starts to wilt.
Add the pasta and the shredded chicken to the pan and toss to coat. Remove the pan from the heat and stir in the heavy cream, if using, and the Parmigiano-Reggiano cheese. Season generously with sea salt and freshly ground pepper.