01 - Bring a large pot of salted water to a rolling boil. Cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water before draining, then set the pasta aside.
02 - While the pasta cooks, season the chicken strips generously with salt and freshly ground black pepper on both sides.
03 - Heat olive oil in a large skillet over medium-high heat. Add the chicken strips and cook for 5 to 7 minutes, turning occasionally, until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and cover loosely with foil.
04 - Reduce the heat to medium in the same skillet. Add the butter and minced garlic, sautéing for about 1 minute until fragrant and lightly softened, being careful not to brown the garlic.
05 - Pour in the heavy cream and whole milk, stirring to combine. Bring to a gentle simmer, then gradually whisk in the freshly grated Parmesan cheese until 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. Incorporate the reserved pasta water a few tablespoons at a time until the sauce reaches your preferred consistency. Season with salt, black pepper, and crushed red pepper flakes if desired.
07 - Sprinkle with chopped parsley, toss gently one final time, and serve immediately. Garnish each portion with additional Parmesan cheese and fresh parsley.