In a Dutch oven or stockpot set over medium heat, add 1 tablespoon of the butter or oil. While heating, sprinkle the chicken with salt and pepper.
Add the chicken and the sun-dried tomatoes to the pan. Sauté until the chicken is cooked through, 5 to 7 minutes. Remove to a plate.
Add the remaining butter to the pan and stir in the garlic, tomato paste, and Italian seasoning. Sauté 2 minutes, until fragrant. Stir in the broth.
Add the cauliflower and bring to a boil. Reduce the heat to a simmer and cook until the cauliflower is tender, about 10 minutes. Transfer to a blender or use an immersion blender and blend until smooth.
Return the soup and the chicken and sundried tomatoes to the pot and bring back to a simmer. Add the spinach and cook until wilted.
Stir in the cream and Parmesan and stir until well combined. Serve with more grated Parmesan sprinkled over.