Cool completely and freeze in airtight storage for up to 3 months. Whisk until well blended. In a large bowl, combine milk. Spray a 13x9" baking dish with nonstick cooking spray. Cornbread Pudding With Caramel Rum Sauce. I made it with my Aunt Jeanâs cornbread sticks! Puddings freeze well. Tear brioche into 1" pieces and place in prepared dish. Serve hot with rum caramel sauce. custard dessert mix, eggs and mutmeg. Stir in nuts and raisins, if using. This is, by far, the best bread pudding Iâve ever eaten. Bread pudding will puff up and appear lightly golden brown on top. To make Rum Caramel Sauce, melt butter in large non stick pan over low heat. Soak the raisins in the rum for at least 5 minutes. Cornbread cubes are placed into lightly greased ramekins. Tear brioche into 1-inch pieces and place in prepared dish. Bake in oven about 25 minutes. Itâs crunchy, tender, slightly sweet and then the rum-infused caramel kicks in and itâs just over the top good! BREAD PUDDING: Preheat oven to 350ºF. Preheat oven to 350 degrees F. Spray a 13 by 9-inch baking dish with nonstick cooking spray. Add brown sugar and cinnamon.