Slice potatos thinly.
Butter pan and preheat oven to 350F.
Place 1/3 of the potato slices in a layer in the pan. The slices should overlap considerably.
Cut the butter into pads about 1/4" thick, then cut them in quarters. Place about six of these pieces spread across the layer. Sprinkle with 1 tb of flour.
Repeat for two more layers
Heat the milk until just below boiling; add the paprika and salt and stir. Pour the milk over the pototos; it should dissolve the flour on the top layer.
Bake for 60 minutes. Remove from oven and cover with a course layer of grated cheese. Bake for another 30 minutes.
Optionally, one can add other incredients between layers. Small pieces of bacon, chives, diced onions or peppers, anchovies, etc. Don't add them to the top layer, just between layers.