Preheat oven to 425°F. Coat a 9x9” casserole dish with oil or butter, set aside.
Using a mandolin or knife, slice the potato into 1/4 inch slices. Slice the cooked corned beef thin and set aside. Slice the shallots and Brussels sprouts thin and set aside.
In a large saucepan add the sliced potato and cover with milk and butter. Bring to a boil, lower heat and simmer 8 minutes. Turn off heat and allow to cool, enough to handle. Reserve the milk and butter, set aside.
Layer the potato then the corned beef slices, shallots and Brussels sprouts. Repeat again using all ingredients.
Whisk the flour into the milk and pour milk over all and top with Parmesan cheese. Bake for 50 minutes. Top will be a deep, crispy brown. Allow to cool at least 15 minutes before slicing to serve.