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Bring a pot of salted water to boil. Place the potatoes in the boiling water and cook for 20 minutes. Drain and set aside.
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Chop the bratwurst into pieces.
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Heat one tablespoon of butter in a medium-sized skillet, add the spring onions and saute for a few minutes.
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Add the bratwurst to the pan, mix to incorporate and fry for 5 minutes, until the bratwurst starts to turn brown. Remove from heat. Transfer the mixture to a plate and set aside. Reserve the pan.
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Grease a casserole dish (I used a 10" round, 3" deep casserole dish)
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Remove the skins from the potatoes and cut into thin slices. Place a layer of potatoes on the bottom of the dish, cover with the bratwurst/spring onion mixture, sprinkle half the cheese on top and cover again with a layer of potatoes.
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Preheat the oven to 425 degrees F.
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Heat the reserved pan. Add the remaining two tablespoons of butter.
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Sprinkle the flour into the pan and stir it around.
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Add the milk and the vegetable broth to the pan and bring to a boil, stirring. Reduce the heat and simmer for 3 minutes.
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Season with Kosher salt and freshly ground pepper to taste.
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Pour the sauce over the potatoes into the casserole dish.
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Evenly distribute the remaining shredded Swiss cheese over the top. Place in the oven and bake for 25 minutes.
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Remove from oven and let cool for 10 minutes before cutting and serving. Garnish with extra spring onion pieces if desired.