Preheat oven to 350°F (175°C). Grease a 9x13 casserole dish.
Parboil sliced potatoes in a pot of water until just tender; drain well.
In a skillet, cook kielbasa and onion until lightly browned.
In a mixing bowl, whisk cream of mushroom soup with milk until smooth.
Layer half the potatoes in the casserole dish, followed by half of the kielbasa-onion mixture and half of the shredded cheeses.
Repeat with the remaining potatoes, sausage mixture, and cheese.
Pour the soup mixture evenly over the layers.
Sprinkle with extra cheese on top for a golden crust.
Bake uncovered for 30–40 minutes, until bubbly and golden brown.
Let rest before serving.
