Pat chicken dry so that it will brown properly. Season chicken on both sides with salt and pepper. Heat a large oven-safe skillet (I used cast iron) on medium heat and add 2 tablespoons of olive oil. When the oil starts to shimmer, add chicken and cook until golden brown on both sides. It will take about 4-5 minutes each.
While the chicken is cooking, shell your pistachios. Try not to eat them all. Add pistachios, basil, parsley, garlic and cheese to a food processor. Blend until the nuts are coarsely chopped, then with the processor on, stream in 1/3 cup of olive oil. I used a bit more than this; the more you add, the more spreadable it will be. It's up to you. Add in 1/4 teaspoon of salt and blend once more. Spread a thin layer of pesto on top of each chicken breast in the skillet, then place in the oven and bake for 15 minutes, or until a meat thermometer reads 165.
Boil the pasta according to package directions. Once finished, drain pasta and toss with remaining 2 tablespoons of olive oil, about 1/4 cup of pesto, the red pepper flakes and grated pecorino. Add more pesto to taste. Once chicken is done, remove and spread a little more pesto on top. Serve with the pasta.