Season the chicken breasts with salt, pepper, and sprinkle Italian seasoning all over.
In a pan or directly in the slow cooker if it has a browning feature, melt the butter with olive oil and cook the chicken skin side down until golden brown.
Flip the chicken breasts and transfer them to the slow cooker if not already there.
Pour in the white wine and water or chicken broth.
Add paprika, garlic granules, chicken bouillon if using wine, and the diced sun-dried tomatoes.
Cover and let the chicken cook on LOW for 90 to 120 minutes until it reaches an internal temperature of 165°F (75°C).
(Optional) Stir in the cornstarch slurry ten minutes before finishing to thicken the sauce, if desired.
Move the chicken to one side and mix in the sour cream or heavy cream thoroughly.
Add grated Parmesan cheese and fresh parsley, stirring everything to combine.
Serve the chicken over your choice of rice, noodles, or mashed potatoes.