Season chicken liberally on both sides. Heat oil in a large skillet over medium heat. Add the chicken and cook undisturbed for 3-4 minutes.
Flip just once, immediately add 1/3 cup chicken stock, reduce heat to simmer and cover pan, allow to cook 5 more minutes. Remove chicken and set aside on a plate tented with foil.
Melt the butter over medium heat into the same skillet (some leftover chicken stock in the pan is fine). Add the minced garlic and cook for 1 minute until fragrant. Add salt and pepper.
Add in 3/4 cup white wine and cook 2 minutes to allow it to reduce slightly. Then add 3/4 cup chicken stock and 3 tablespoons lemon juice. Slowly pour in the half and half then bring to a gentle boil. Add the pasta into the pan, breaking in half if needed or allow them to heat so you can bend them into the pan using tongs.
Allow pasta to simmer for 4-5 minutes, stirring frequently, then reduce heat to low and continue to simmer until pasta is al dente.
Add the parmesan gradually, reserving some for serving. The sauce will continue to thicken as the dish sits.
Sprinkle with fresh parsley, lemon zest, red pepper flakes. Toss well and serve with sliced chicken and parmesan on top.