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 freshly ground black pepper on all sides.
03 - Heat the olive oil in a large skillet over medium-high heat until shimmering. 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 heat to medium in the same skillet. Add the butter and allow it to melt, then add the minced garlic. Sauté for about 1 minute, stirring frequently, until fragrant and lightly golden. Do not let the garlic 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. Continue stirring until the cheese is fully melted and the sauce is smooth and velvety.
06 - Add the cooked pasta and seared chicken to the skillet, tossing everything together to coat evenly in the sauce. Add the reserved pasta water a splash at a time 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 parsley and toss gently. Serve immediately, garnished with additional freshly grated Parmesan and parsley leaves.