Season both sides of the chicken breasts with salt and pepper. Heat 1⁄2 tablespoon of olive oil in a large skillet over medium-high heat and brown the chicken breasts on both sides for about 4 minutes on each side. Transfer to a plate and keep warm.
Reduce the heat to medium and add the remaining ½ tablespoon of oil. Saute the minced garlic until fragrant, about 30 seconds. Pour the white wine and deglaze the skillet scraping the bottom to remove all the bits and pieces stuck to it. Cook until reduced by half.
Pour in the chicken broth, heavy cream, Italian seasoning and Parmesan cheese and simmer until the sauce starts to thicken.
Add the chopped spinach and sundried tomatoes and cook until the spinach starts to wilt. Check the seasoning and add salt and pepper if needed.
Return the chicken breasts to the skillet and spoon the sauce over them. Cook for a couple of minutes more until they are heated through.