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 it aside.
02 - While the pasta cooks, pat the chicken strips dry and season both sides generously 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 once, 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 heat to medium. Add the butter to the same skillet along with the minced garlic. Sauté for about 1 minute, stirring constantly, until the garlic is fragrant and lightly golden. Do not let it brown.
05 - Pour in the heavy cream and milk, stirring to combine. Bring the mixture to a gentle simmer, then gradually whisk in the Parmesan cheese a handful at a time until fully melted and the sauce is silky smooth.
06 - Add the drained pasta and seared chicken back into the skillet. Toss everything together, coating the pasta and chicken evenly in the sauce. If the sauce seems too thick, add the reserved pasta water a splash at a time until it reaches your preferred consistency. Season with salt, black pepper, and crushed red pepper flakes if desired.
07 - Sprinkle with the chopped parsley, toss gently one last time, and serve immediately. Garnish each portion with additional grated Parmesan and a few parsley leaves.