PREHEAT oven to 350° F. Grease a 2-quart casserole or baking dish.
PLACE bread cubes in prepared baking dish. Combine sugar, cocoa and coffee granules in a small bowl.
BEAT eggs, 2-2/3 cups evaporated milk and vanilla extract in a medium bowl until well blended; stir in sugar mixture. Pour over bread, pressing bread into milk mixture.
BAKE for 50 to 55 minutes or until set.
COMBINE brown sugar, butter and corn syrup in a small heavy-duty saucepan. Cook over medium-low heat, stirring constantly, for 2 to 3 minutes or until sugar is dissolved. Slowly stir in remaining evaporated milk. Bring to a boil, stirring constantly; cook for 1 minute. Remove from heat. Serve with warm bread pudding.