Preheat a large skillet over medium high heat and add the 1 tablespoon of butter. Season the chicken with salt and pepper and add to the skillet.
Cook chicken until golden brown, about 8 minutes. Flip and cook until the other side is brown and chicken is cooked through, another 5-8 minutes. Remove chicken from the pan and let cool slightly, then slice and set aside.
Reduce heat to medium low and add remaining ½ cup butter and heavy cream, stirring to combine. Stir in 1 cup of the parmesan cheese.
Meanwhile, while you prepare the chicken and sauce, cook the fettuccine in a large pot of salted water until al dente. Drain, reserving 1 cup of the cooking liquid.
Add the fettuccine and sliced chicken breast to the skillet with the remaining 1 cup of cheese. Toss until well coated with the sauce. Add the cooking liquid a little at a time if needed to loosen up the sauce. Serve immediately.