Preheat the oven to 375ºF.
Coat the inside of the casserole with butter and lightly dust with flour.
In a small saucepan on medium heat, melt 2 tablespoons of the butter and once foaming, add the flour and whisk until there are no lumps. Add a little of the milk, whisking all the while to keep lumps from forming. Then, slowly add the rest of the milk, continuing to stir. Bring to a simmer and continue simmering for about five minutes while stirring fairly regularly.
While the milk is simmering, peel and thinly slice the blue potatoes.
Once the milk has simmered for about 5 minutes and thickened, fold in the cheese a spoonful or two at a time. Once fully incorporated, turn off the heat, then mix in the nutmeg, salt and pepper.
Put a layer or two of potatoes on the bottom of a 9 inch oval casserole. Pour on a bit of the cheese sauce, and then add another layer of potatoes. Repeat with alternating layers of cheese sauce and potatoes until the casserole is filled. On the top layer of potatoes, dot with the remaining 2 tablespoons of butter. Cover with aluminum foil.
Bake for 45 minutes until tender.
Remove the foil and put under the broiler for 5 minutes until golden brown.
Serves 4 to 6.