2. Remove the potatoes from the oven and split open with a knife. When cool enough to handle, scoop out the flesh with a spoon and transfer it to a processor. Process the potato flesh with a tablespoon of the butter, milk and salt and pepper to taste.
3. Meanwhile, peel, core and slice the apples into 1/4-inch slices. Heat the remaining tablespoon of butter in a large skillet over medium heat. Add the brown sugar. Stir and cook until the sugar has melted, about 3 minutes. Add the cinnamon and apple slices. Cook until slightly softened and coated with the caramel, about 3 to 4 minutes.
4. Transfer the potato puree into a shallow baking dish and smooth the top with a spatula. Arrange the apple slices over the puree in an overlapping pattern. Transfer the puree to the oven and bake until throughly heated, about 10 minutes. Serve hot.
(This recipe can be made up to two days ahead and stored in the refrigerator, covered with plastic wrap. Remove from the refrigerator 30 minutes before heating.)