Cook pasta (16 ounces) according to package instructions in well-salted water. Drain.
Pat chicken breast (2) dry with paper towels. Season generously with salt and pepper.
Heat the olive oil (2 tablespoons) over medium-high heat, in a 12-inch skillet. Cook chicken breasts in the hot skillet until golden brown, about 5-7 minutes without flipping them or moving them in the pan. Turn breasts over and add 2 tablespoons of butter. Cook the breast for another 5-7 minutes or until an instant thermometer reads 165 °F (74 °C). Do not overcook or the chicken will be dry. Remove to a plate and allow to rest for 7-10 minutes. Slice chicken and cover with aluminum foil; set aside.
In a clean large, high-sided skillet, melt the remaining 1/2 cup butter over medium-low heat and saute garlic (1 tablespoon) until fragrant, about a minute. Sprinkle flour (2 tablespoons) over butter and cook, whisking constantly for 1 minute. Remove pan from heat and slowly whisk in cream (2 cups) and milk (1 cup) until smooth.
Return skillet to medium-low heat and stir in 3/4 cup Parmesan cheese and white pepper (1/8 teaspoon) and simmer gently until cheese is melted.
Toss cooked pasta with sauce. (At first, the pasta may seem soupy but, as it sits, the pasta will quickly absorb more sauce and you will have plenty of sauce to coat the pasta generously and it won't be dry when you go back for seconds!) Arrange pasta on plates and top with sliced chicken. Sprinkle with parsley (2 tablespoons) and serve extra Parmesan on the side.
Notes
Chicken - Be sure to let your cooked chicken restbefore slicing it up. This is very important! If you cut it too soon, all the juices will run out and you’ll end up with dry rubbery chicken.
Toast the Flour: You’ll want to sauté the flour in the butter/garlic mixture for just a minute and remove it from heat. This is another critical step.
First, it helps coat the flour in butter, so it acts the way we want it to, and it gets rid of that flour flavor. Removing it from heat stops it from cooking so you end up with a white roux. Here’s a little about the different types of roux, just in case.