In a large mixing bowl, beat the eggs. Add all the ingredients except the bread and pecans. Mix well until everything is combined.
Fold in the cubed bread and half of the pecans. Let the mixture sit at room temperature for 1 hour, stirring occasionally. For best results, refrigerate the mixture for 6-8 hours or overnight.
Preheat the oven to 350 degrees. Prepare a baking dish with butter or cooking spray. Pour the mixture into the dish and top it with the remaining pecans. Bake for 60 minutes.
While the bread pudding is baking, melt the butter in a saucepan. Add sugar, rum or bourbon, and water. Simmer the mixture for 10 minutes, then let it sit to keep warm until the bread pudding is done.
Once the bread pudding is ready, pour half of the rum sauce over the top while it's still hot. Let it sit for 15 minutes, then add more sauce as desired. Serve warm with vanilla ice cream or fresh whipped topping.