Preheat oven to 375°F Grease a baking pan just large enough to hold the apples.
With a small knife, cut at an angle to enlarge the core opening at the stem end of each apple to about 1 inch diameter. (The opening should look like a funnel shape.).
Arrange the apples in the prepared pan, stem end up.
In a small saucepan, combine 3/4 cup water with brown sugar, nutmeg and pepper. Bring the mixture to a boil, stirring. Boil for 6 minutes.
Combine the walnuts and raisins. Spoon some of the walnut/raisin mixture into opening of each apple.
Top each apple with some of the diced butter.
Spoon the brown sugar sauce over and around the apples. Bake, basting occasionally with the sauce, until the apples are just tender, 45-50 minutes. Transfer the apples to a serving dish, reserving the brown sugar sauce in the baking pan. Keep the apples warm.
For the caramel sauce, mix the butter, cream and reserved brown sugar sauce in a saucepan. Bring to a boil, stirring occasionally, and simmer until thickened, about 2 minutes. Let the sauce cool slightly before serving.