01 - Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Reserve 1/2 cup of the starchy pasta water before draining. Set the drained pasta aside.
02 - While the pasta cooks, season the chicken strips evenly with salt and freshly ground black pepper on both sides.
03 - Heat the olive oil in a large skillet over medium-high heat. Arrange the chicken strips in a single layer and cook for 5 to 7 minutes, turning once, until deeply golden and cooked through to an internal temperature of 165°F. Transfer the chicken to a plate and tent loosely with foil to keep warm.
04 - Reduce the heat to medium. Add the butter and minced garlic to the same skillet, sautéing for about 1 minute until the garlic is fragrant and softened, taking care not to let it brown.
05 - Pour in the heavy cream and whole milk, stirring to combine. Bring the mixture to a gentle simmer, then gradually whisk in the Parmesan cheese until fully melted and the sauce is silky smooth.
06 - Add the drained pasta and seared chicken to the skillet, tossing everything together until evenly coated. Splash in the reserved pasta water a little at a time until the sauce reaches your preferred consistency. Season with salt, black pepper, and red pepper flakes if desired.
07 - Sprinkle with the chopped parsley, toss gently one final time, and serve immediately. Garnish each portion with additional shaved Parmesan and a sprig of fresh parsley.