1Grease 13x9 inch oblong pan with butter; set aside. Adjust oven rack to middle position and preheat oven to 350°F. Place bread cubes in large bowl.
2In medium saucepan whisk milk and sweetened condensed milk combine. Heat over medium heat, stirring occasionally, until scalding. Remove from heat and whisk in chocolate until melted and smooth.
3In small bowl, whisk vanilla and eggs to combine. Slowly whisk 1/2 cup warm milk mixture into egg mixture to combine. Whisk this mixture back into milk mixture. Pour 1/2 mixture over bread cubes and let soak into bread, stir gently. Pour into pan. Sprinkle pecans over top.
4Combine cream and sugar for caramel sauce. Heat milk and sugar until sugar melts. Stir in remaining ingredients. Drizzle over pudding. Pour remaining milk mixture over caramel.
5Cover with foil and bake approximately 1 hour. Remove foil and continue to bake until slightly brown, about 15 min.
6While pudding cools slightly, make rum sauce.
7Combine powered sugar and rum. Drizzle over warm pudding. Serve warm.