Preheat your oven to 350°F (175°C).
In a skillet over medium heat, add the olive oil. Once hot, add the chopped onion and sliced kielbasa. Sauté for about 5 minutes or until the onions are translucent and the kielbasa is lightly browned.
In a large mixing bowl, combine the sliced potatoes, sautéed onion and kielbasa mixture, garlic powder, paprika, salt, and pepper. Mix well to incorporate all the ingredients.
In another bowl, whisk together the sour cream and milk until smooth. Pour this mixture over the potato and sausage mixture and stir until everything is evenly coated.
Transfer the mixture into a greased 9x13 inch baking dish. Spread it out evenly.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and sprinkle the shredded cheddar cheese evenly on top. Return to the oven and bake for an additional 15 minutes, or until the cheese is melted and bubbly and the potatoes are tender.
Once done, remove the casserole from the oven and allow it to cool for a few minutes. Garnish with chopped parsley if desired, and serve warm.