Halve kielbasa lengthwise, and slice into ⅓-inch-thick slices. Heat oil in a large skillet over medium-high. Add kielbasa slices, onion and caraway seeds; cook, stirring occasionally, until kielbasa is browned and onion is tender, about 8 minutes.
Add butter to skillet; cook over medium-high, stirring constantly, until melted, about 20 seconds. Add cabbage, apple, pepper and salt; cover and cook, stirring occasionally, until cabbage and apple are tender and browned, about 10 minutes. Uncover. Stir in garlic; cook, stirring constantly, until fragrant, about 1 minute. Remove from heat. Stir in mustard and vinegar. Sprinkle with parsley and paprika.
