Preheat the oven to 350 degrees F. Brush or spread the butter over the bottom and sides of a 2-quart flame-proof baking dish.
Fill the prepared baking dish with the cubed bread. In a large bowl, whisk together the milk, eggs, 1/2 cup sugar, vanilla, cinnamon and salt. Pour the liquid mixture over the bread, turning the cubes gently with a spatula so the bread is coated. Let sit for 10 minutes so the bread absorbs the custard mixture.
Press down gently with a spatula to distribute the custard and bread evenly in the dish. Bake for until the pudding is set in the center but still very moist and the top is lightly browned, 30 to 45 minutes.
Meanwhile, mix together the remaining 2 tablespoons sugar with the smoked paprika in a small bowl. When the pudding is set, remove it from the oven. Preheat the broiler. Top the pudding with an even layer of the potato chips and sprinkle with the sugar and paprika mixture. Broil until the top is toasted and deeply golden. Cool for 10 minutes; serve warm.