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 generously with salt and black pepper on all sides. Heat the olive oil in a large skillet over medium-high heat until shimmering. Arrange the chicken in a single layer and cook for 5 to 7 minutes, turning once, until deeply golden and cooked through to 165°F. Transfer the chicken to a plate and tent loosely with foil to keep warm.
03 - Reduce the heat to medium. In the same skillet, melt the butter. Add the minced garlic and sauté for about 1 minute, stirring constantly, until fragrant and lightly golden — do not let it brown.
04 - Pour in the heavy cream and milk, stirring to combine. Bring the mixture to a gentle simmer — do not boil. Gradually whisk in the Parmesan cheese a handful at a time, allowing each addition to melt smoothly before adding more. The sauce should be velvety and cohesive.
05 - Add the drained pasta and seared chicken back into the skillet. Toss everything together, coating the pasta and chicken evenly in the sauce. 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. Sprinkle with chopped parsley, toss gently once more, and serve right away with extra Parmesan and parsley on top.