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. Before draining, reserve 1/2 cup of the starchy pasta water. Drain the pasta and set aside.
02 - While the pasta cooks, season the chicken strips generously on all sides with salt and freshly ground black pepper.
03 - Heat the olive oil in a large skillet over medium-high heat. Add the seasoned chicken strips in a single layer and cook for 5 to 7 minutes, turning occasionally, until golden brown 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 skillet heat to medium. Add the butter and minced garlic, sautéing for about 1 minute until fragrant and lightly golden, stirring constantly to prevent burning.
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 back into the skillet, tossing everything together to coat evenly. Splash in the reserved pasta water a little at a time, tossing between additions, until the sauce reaches your preferred consistency. Season to taste with salt, black pepper, and crushed red pepper flakes if desired.
07 - Sprinkle with chopped fresh parsley and toss gently one final time. Serve immediately in warmed bowls, garnished with additional shaved Parmesan and parsley leaves.