Heat the butter and oil in a large nonstick skillet over medium-high heat. Season pork chops with 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Saute for 3 minutes per side until nicely browned. Remove to a plate and keep warm.
Add sliced cabbage, shredded carrot, wine, caraway seeds, thyme and remaining salt and pepper to the skillet. Stir to combine.
Cover and cook for 8 minutes over medium-high heat, stirring occasionally.
Add sliced kielbasa and vinegar to the skillet. Tuck the browned pork chops back into the mixture.
Cover skillet and cook on medium-low heat for 5 minutes, stirring occasionally or until pork chops reach internal temperature of 155 degrees F as measured on an instant-read thermometer. Turn off heat. Allow to rest for 5 minutes before serving. Makes 4 servings.