Brown the chicken. Pat the chicken dry and season with the salt and pepper. Heat the oil in a 5- to 6-quart pot over medium heat. Brown the chicken in batches if needed, about 4 to 5 minutes total per batch. Transfer to a plate; it will finish cooking in the broth.
Cook the onion. Add the butter and onion to the same pot. Cook for about 4 minutes, stirring, until softened. Lower the heat if the browned bits begin to scorch.
Build the flavor. Add the garlic, sun-dried tomatoes, tomato paste, Italian seasoning, and optional red pepper flakes. Cook for 1 minute, stirring constantly.
Add broth and pasta. Pour in the broth and scrape up the browned bits. Bring to a boil. Return the chicken and its juices to the pot, add the pasta, and reduce to a gentle simmer.
Simmer. Cook uncovered for 8 to 12 minutes, or according to the pasta package timing, stirring often. The pasta should be just tender and the largest chicken pieces must reach 165°F.
Add cream and spinach. Reduce the heat to low. Stir in the cream and spinach. Warm gently for 1 to 2 minutes, until the spinach wilts.
Finish and serve. Remove from the heat. Stir in the Parmesan in small handfuls, then add the basil and optional lemon juice. Taste and adjust salt and pepper. Add warm broth if needed and serve promptly.