Mix brown sugar, butter, cinnamon, and nutmeg together in a bowl.
Cut the core out of each apple leaving the bottom intact to form a well. Stuff each apple with the brown sugar mixture, filling almost to the top. Place a few blueberries on top of the filling and finish with a layer of brown sugar mixture. Press a few raisins into the brown sugar mixture.
Pour enough water into a shallow baking dish to cover the bottom; add walnuts, rum, vanilla extract, and cornstarch and mix well.
Arrange apples in the water mixture and cover the dish with aluminum foil.
Bake in the preheated oven until apples are slightly tender, about 20 minutes. Remove foil and bake until sugar begins to caramelize, water mixture is thickened, and apples are tender, about 15 minutes more. Stir the water mixture and spoon it over the apples. Cool apples for about 5 minutes before serving.