Drain the sun-dried tomatoes in a colander and turn them out onto a double layer of paper towels. Pat them with more paper towels to remove the excess oil. Thinly slice them and set them aside. You should have about ½ cup.
Add 2 tablespoons of olive oil to a deep 12-inch skillet or sauté pan and place it over MEDIUM heat. Add the chopped chicken and season with the Italian seasoning, smoked paprika, ½ teaspoon salt, and ¼ teaspoon pepper. Cook, stirring frequently, 4 to 5 minutes or until the chicken is completely cooked through. Transfer the chicken to a plate and cover to keep warm.
Add a little additional oil to the pan, if needed, and add the onions. Cook for 2 or 3 minutes, until softened and lightly browned. Add the garlic and cook for a minute until fragrant. Add the tomato paste and cook, stirring for a minute or two. Then add the broth, sun-dried tomatoes, pasta, and the remaining ¼ teaspoon salt and pepper and stir to combine. Stir in the cooked chicken and bring to a boil, cover the skillet, and reduce the heat to MEDIUM-LOW. Simmer (it should be bubbling a little) until the pasta is tender, about 15 minutes.
Remove the cover and reduce the heat to LOW. Stir in the half and half, cherry tomatoes, and ½ cup Parmesan cheese and simmer for a minute or two until warmed through and the cheese has melted. Add the spinach and use a spoon to fold it into the pasta mixture. As soon as the spinach begins to wilt, remove the skillet from the heat and continue to stir until the spinach is wilted and well incorporated. Top with fresh basil (if using) and remaining Parmesan and serve with additional Parmesan on the side.