Prepare the Sun-Dried Tomatoes: Drain 3 tablespoons of oil from the sun-dried tomato jar into a large pot or deep-sided skillet, then chop the sun-dried tomatoes and set them aside.
Season the Chicken: Add the cubed chicken to the pot over medium-high heat, then season it with 3 teaspoons of the Italian seasoning, the paprika, a pinch of red pepper flakes, and a pinch each of kosher salt and black pepper.
Brown the Chicken: Cook the seasoned chicken for about 5 minutes, turning as needed, until it becomes golden brown. Add 1/4 cup of the grated Parmesan and cook for 1 minute longer. Set Aside the Chicken: Remove the cooked chicken from the pot and set it aside, keeping any juices that remain on the plate.
Build the Flavor Base: Add a drizzle of oil to the same pot along with the salted butter. Stir in the chopped shallot, garlic, Calabrian chili paste, and the remaining 1 teaspoon of Italian seasoning. Cook the Aromatics: Cook the shallot, garlic, chili paste, and seasoning for about 3 minutes, until fragrant.
Cook the Pasta: Pour 3 1/2 cups water into the pot and bring the mixture to a boil. Add the short-cut pasta and cook for about 8 minutes, stirring often, until the pasta reaches an al dente texture.
Finish the Creamy Sauce: Stir in the heavy cream, fresh baby spinach, chopped sun-dried tomatoes, and the remaining 3/4 cup Parmesan cheese, combining everything until incorporated.
Return the Chicken: Slide the cooked chicken back into the pot along with any juices left on the plate, allowing it to combine with the pasta and creamy sauce.
Serve: Spoon the finished pasta into serving dishes and top with fresh Parmesan and basil.
