Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Drain and set aside.
Heat olive oil in a large skillet over medium-high heat. Season the chicken with salt and pepper. Add to the pan and cook until browned and cooked through, about 5–7 minutes. Remove and set aside.
In the same skillet, add sliced chorizo. Cook for 3–4 minutes until it starts to crisp and release its oils. Remove and set aside with the chicken.
Add chopped onion to the skillet and cook for 2–3 minutes until softened. Stir in garlic, smoked paprika, and chili flakes. Cook for another minute.
Add tomato paste and stir well. Pour in chicken broth and bring to a simmer. Stir in the heavy cream and Parmesan cheese. Let the sauce simmer for 4–5 minutes until thickened.
Return the cooked chicken and chorizo to the skillet. Add the drained pasta and toss until well combined and coated in the sauce.
Garnish with chopped parsley if desired. Serve hot and enjoy immediately.