Bring a large pot of salted water to a rolling boil.
Meanwhile, season the chicken breasts with salt & pepper. Add the butter & olive oil to a medium skillet over medium-high heat until the butter is melted. Swirl the pan to coat evenly and add the chicken breasts. Cook 6-8 minutes on each side, until the outside of the breasts are golden and the chicken reaches an internal temperature of 165 degrees Fahrenheit. Remove the chicken from the skillet to a plate, and let cool.
As the chicken cools, add the spaghetti to the pot of boiling water & cook according to package directions.
While the pasta cooks, make the pesto. Place the basil, parmesan cheese, sunflower seeds, garlic, olive oil, salt, & pepper in a small food processor. Blend until smooth.
When the pasta is done cooking, drain & place in a large serving bowl. Shred the chicken breasts into bite sized strips and add to the bowl with the pasta. Pour the pesto over top & mix well by tossing with 2 large forks.
Plate each individual serving, sprinkle with extra cheese, fresh cracked pepper, and flaky maldon sea salt. Enjoy with a nice side salad.