Boil water in a large pot, add salt, and cook the pasta according to package instructions until al dente. Reserve a cup of pasta water, then drain the rest.

In a large skillet, heat the olive oil over medium heat. Add the thinly sliced chicken, seasoning with salt and pepper. Cook until golden brown and cooked through, about 5-7 minutes. Remove chicken and set aside.

In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Pour in the heavy cream (or cream and milk mixture) and allow it to simmer for a couple of minutes. Stir in the grated Parmesan cheese until melted and smooth.

Return the cooked chicken to the skillet and add the drained pasta. If the sauce seems too thick, gradually add some reserved pasta water until desired consistency is reached. Mix thoroughly.

Serve the pasta hot, with extra Parmesan on top if desired, and a squeeze of lemon or a pinch of nutmeg for an extra flavor punch.