CUT the leftover cake into 1-inch cubes and lay them single file on a sheet pan. If they were frozen, give them an hour or more to come to room temperature. If you have time, leave the cake cubes out for several hours (overnight is best) so they get a bit stale.
PREHEAT a skillet over medium heat until warm.
ADD the pecans and cook, stirring every couple of minutes to prevent burning.
COOK for about 5 minutes. The pecans should get toasty and smell fabulous.
TAKE the pan from the heat and let the nuts cool down until they can be handled.
ROUGHLY CHOP the pecans with a sharp knife on a cutting board. Set them aside until needed.
PREHEAT the oven to 350°F (175°C).
POUR the dry cake cubes into a large mixing bowl.
REMOVE the egg from the fridge and place it in a small bowl filled with warm water to quickly bring it to room temperature.
HEAT the milk and butter in a small saucepan on the stove over medium heat until the butter is melted. The milk should get steamy but never come to a boil. Set it aside.Note: Use the microwave if you prefer. Pour the milk and butter into a microwave-safe bowl and heat for 1 minute. Stir until the butter melts. If necessary, heat again at 10-second intervals.
COMBINE the sugar, egg, and vanilla extract with a wire whip. Stir a couple of tablespoons of the milk mixture into the egg mixture to temper it (so the egg doesn't cook).
SPRINKLE in the cinnamon, nutmeg, and salt.
ADD the rest of the milk/butter combo and stir until combined.
POUR the mixture into the dry cake cubes. Stir until a lot of the liquid is absorbed by the cake. Add the toasted pecans and dried fruit.
REST for 15 to 20 minutes for maximum moisture absorption.Note: Some excess liquid is fine when the pan goes into the oven. Too much liquid, and it will get soggy and taste eggy. If you have too much liquid for the amount of cake cubes, drain some off before baking it.
SPREAD a thin layer of butter or shortening in an 8 X 8-inch casserole dish.
POUR the cake mixture into the bottom of the dish.
BAKE for 30 to 40 minutes. The sweet dessert will look moist but not soggy when it is done. A toothpick stuck in the center will come out mostly clean. Don’t overbake, or it will taste dry.
MAKE the brown sugar sauce while the pudding is baking. Combine the butter and brown sugar in a small saucepan. Heat over medium heat until the butter melts and the mixture boils.
TURN the stove down to low heat and continue to cook until the sugar melts.
REMOVE the pan from the burner and turn off the stove. Set it aside.
TAKE the cake bread pudding from the oven.
DRIZZLE the sauce on top of the bread pudding right after it comes out of the oven.
COOL for 5 minutes. Then top with a scoop of vanilla ice cream.