Cook the pasta: Bring a large pot of salted water to a boil. Cook penne until just al dente according to package directions.
Reserve 1 cup of pasta water, then drain.
Season the chicken: Pat chicken dry. Toss with 1 tablespoon olive oil, 1 teaspoon salt, 1/2 teaspoon black pepper, 1 teaspoon smoked paprika, 1 teaspoon Italian seasoning, and 1 teaspoon red pepper flakes.
Sear the chicken: Heat remaining 1 tablespoon olive oil in a large skillet over medium-high. Cook chicken in a single layer, 3–4 minutes per side, until golden and cooked through.
Transfer to a plate; tent with foil.
Build the sauce base: Reduce heat to medium. Add butter to the skillet. Stir in garlic; cook 30 seconds until fragrant.
Pour in chicken broth, scraping up browned bits. Simmer 1–2 minutes.
Add cream and spice: Stir in heavy cream and another 1/2–1 teaspoon red pepper flakes (to taste). Bring to a gentle simmer; do not boil hard.
Melt the cheese: Reduce heat to low.
Gradually whisk in Parmesan, a handful at a time, until smooth. If the sauce seems too thick, add a splash of reserved pasta water to loosen.
Combine: Add cooked penne and the chicken (with juices) to the skillet. Toss to coat.
Add lemon zest and a squeeze of lemon juice. Adjust seasoning with salt and pepper. If you like extra heat, finish with a dash of hot sauce or a pinch of cayenne.
Finish and serve: Sprinkle with chopped parsley.
Serve immediately, with extra Parmesan and red pepper flakes on the table.