Season the chicken breasts with salt, pepper, and Italian seasoning.
Heat the butter and olive oil (if using) in a pan or directly in the slow cooker if it has a browning function. Sear the chicken skin-side down until golden.
Turn the chicken over and pour in the white wine or chicken broth. Add the sun-dried tomatoes.
Cover the slow cooker and cook on LOW for 90 minutes to 2 hours or until the chicken reaches an internal temperature of 165°F (75°C).
Once cooked, remove the chicken to one side. Stir in the sour cream or heavy cream and Parmesan cheese to make the sauce creamy.
Garnish with fresh parsley or basil and serve over pasta, rice, or mashed potatoes.
