Preheat the oven to 350 degrees F. Butter a 9-by-13-inch casserole dish with 1 tablespoon butter. Melt the remaining 2 tablespoons 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, stirring 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.
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, or until the potatoes and cheese are golden and browned. Let stand 15 minutes before serving.