Lightly season the chicken breasts with salt, pepper, and Italian seasoning on both sides.

In a pan, or directly in your slow cooker if it has a browning function, melt the butter along with olive oil. Place the chicken skin side down and sear until the surface becomes golden.

Once browned, flip the chicken and transfer to the slow cooker if necessary. Pour in the white wine and water mixture or chicken broth. Sprinkle with sweet paprika, garlic granules, and chicken bouillon if applicable. Toss in the diced sun-dried tomatoes.

Cover and let the chicken cook on the LOW setting for 90 minutes to 2 hours, or until the internal temperature reaches 165°F (75°C).

If desired, prepare a cornstarch slurry by mixing cornstarch with cold water. Stir this into the sauce about 10 minutes before cooking time ends to thicken the sauce.

Once the chicken is fully cooked, move it to one side and turn slow cooker to warm. Stir in the sour cream or heavy cream until fully blended, then incorporate the grated Parmesan and freshly chopped parsley or basil.

Serve the chicken accompanied by your choice of rice, pasta, or mashed potatoes.