In a large pot, heat the sun dried tomato oil from the jar and the salted butter over medium heat until the butter melts.
Add the finely chopped shallot and cook, stirring often, until softened, about 3 minutes.
Add the chopped, drained julienne-cut sun dried tomatoes, tomato paste, and the chopped garlic. Cook, stirring, until the tomatoes begin to break down, about 2 minutes.
Pour in the chicken broth, then stir in the packed chopped fresh spinach, the packed shredded rotisserie chicken, and the salt. Stir to combine.
Increase heat to bring the soup to a boil, then reduce the heat to maintain a simmer. Cook uncovered, stirring occasionally, for about 10 minutes.
Remove the pot from the heat. Stir in the grated Parmesan cheese, the heavy whipping cream, and the cream cheese (cut into small cubes). Continue stirring until the cream cheese is fully melted and the soup is smooth.
Stir in the chopped fresh basil.
Serve the soup and garnish each bowl with additional grated Parmesan cheese and fresh basil.