Preheat the oven to 350 degrees . In a large skillet, melt 1 tablespoon butter over medium-high heat. Add half of the cabbage, half of the potatoes and 1 1/2 teaspoons caraway seeds; cook, stirring often, until the cabbage is slightly wilted and the potatoes are crisp-tender, about 5 minutes. Transfer to a 9-by-13- inch baking dish and top with half of the corned beef. Repeat with another tablespoon of butter and the remaining cabbage, potatoes and caraway seeds; transfer to the baking dish and top with the remaining corned beef.
In a medium saucepan, melt the remaining 4 tablespoons butter over medium heat. Whisk in the flour and cook, stirring, for 2 minutes. Whisk in the milk gradually and cook, stirring, until the sauce is smooth and thickened, 5 to 7 minutes; season with salt and pepper. Pour the sauce over the casserole and spread evenly with a knife. Top with the potato chips and bake until golden-brown and bubbling, about 25 minutes.