Preheat oven to 350 degrees. Butter a 9 x 13-inch casserole dish with 1 T. butter. Melt the remaining 2 T. butter in a large saucepan. Once the butter foams, add the shallot and garlic and saute until softened, 3 to 4 minutes. Add the flour and cook, sitrring frequently, until golden, about 2 minutes. Season with salt and pepper and add the half-and-half, smoked paprika and potatoes. Bring to a low simmer and cook for 5 minutes.
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Pour half of the potato mixture into the buttered casserole dish. Shake the pan to arrange the potatoes in a single layer. Sprinkle half of each of the cheeses on top of the bottom potato layer. Add the remaining potatoes and shake again to arrange in a layer. Sprinkle on the remaining cheese, cover with foil and bake 45 minutes, or until bubbling. Remove the foil and place back in the oven for another 15 minutes before serving.
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