Cook the penne in well-salted water until just shy of al dente. Reserve 1 cup of the starchy pasta water, then drain. (That cloudy water is liquid gold for sauces.)
Pat the chicken strips very dry and season with salt, pepper, and Italian seasoning. Dry chicken sears; wet chicken steams.
Heat the olive oil and 2 tbsp butter in a large skillet over medium-high heat. Sear the chicken 3 to 4 minutes per side until golden and cooked through (165°F). Transfer to a plate.
In the same skillet, melt the remaining 2 tbsp butter. Add the garlic and red pepper flakes; cook 30 seconds until fragrant.
Pour in the cream and simmer 2 to 3 minutes, scraping up the browned bits. Off the heat, whisk in the parmesan a handful at a time until smooth. (Off the heat — hot cream plus cold cheese can turn grainy.)
Return the chicken and pasta to the skillet. Toss with a splash of pasta water until glossy. Shower with parsley and extra parmesan.