Boil the pasta according to the package instructions. Once cooked, drain the pasta being sure to reserve about 250ml (1 cup) of the pasta water. Set aside.
Heat a cast iron or non stick frying pan over medium hight heat and add the tablespoon of olive oil. Season the chicken well with sea salt. Once the pan and oil are hot (the oil will shimmer) place the chicken thighs in the pan and sear for about 6 minutes on each side until the chicken is cooked through. Use a thermometer to make sure the chicken temperature is at least 75c or 165f.
Remove the chicken from the pan and set aside.
To make the sauce, add the 2 tablespoons of butter to the same pan that you seared the chicken in. Do this over medium heat. *see notes. Melt the butter in the pan. Once the butter is melted, add in the minced garlic and cook for about 5 minutes until the garlic is softened and fragrant. Pour in the chicken stock or water and scrape any brown bits from the bottom of the pan. Bring to a gentle simmer.
Stir in the lemon juice and zest. In a slow steady stream pour in the single cream. Add in the grated parmesan and simmer gently for about 5 minutes whisking continuously. Taste and adjust the seasoning. Stir in the chopped parsley and basil and add in the crushed chilli flakes if using. Toss the cooked pasta into the sauce and pour in any pasta water to get the desired consistency.
Slice the chicken thighs and place on top of the pasta to serve. Add the chicken juices back to the pan.