Place the 1½-inch potato pieces and chopped onion in the bottom of a 6-quart slow cooker.
Add the olive oil, salt, pepper, and Cajun seasoning. Toss to coat. Layer the sliced fully cooked kielbasa and fresh green beans over the potatoes.
Sprinkle the dry onion soup mix and garlic powder evenly over the ingredients. Distribute the butter pieces across the top.
Cover and cook on Low for 6–7 hours, stirring a few times. Begin checking at 5 hours. The dish is ready when a fork or knife enters the potatoes easily while the pieces still hold their shape. Stir gently and serve warm.