Cook the pasta according to the package instructions. Reserve 1/2 cup of pasta water before draining.
Heat olive oil in a large skillet over medium heat. Add chicken and cook until golden brown. Remove from skillet and set aside.
In the same skillet, sauté onion and garlic until fragrant. Stir in crushed tomatoes, red pepper flakes, smoked paprika, salt, and pepper.
Simmer the sauce for 10 minutes, then stir in heavy cream.
Add the cooked chicken back into the skillet and toss to coat with the sauce.
Mix in the cooked pasta and reserved pasta water to loosen the sauce if needed.
Serve hot, garnished with parsley and grated Parmesan.