Season chicken with 1 tsp salt, black pepper, paprika, and Italian seasoning.
Heat olive oil and butter in a large pot over medium-high. Sear chicken until lightly browned, 4–5 minutes. Transfer to a plate.
Sauté onion in the same pot until softened, about 3 minutes. Stir in garlic and sun-dried tomatoes; cook 30 seconds.
Pour in chicken broth and heavy cream, scraping up any browned bits. Bring to a gentle boil.
Add pasta and return chicken to the pot. Stir well and reduce to a lively simmer.
Simmer uncovered, stirring occasionally, until pasta is al dente and chicken is cooked through, 12–14 minutes.
Lower heat. Fold in Parmesan and spinach until creamy and wilted. Adjust with remaining salt and red pepper flakes.
Let rest 2 minutes to thicken. Top with basil and extra Parmesan before serving.