Line a 12-inch square pan with sliced French bread and dry in oven for 10 minutes at 350°F.
Combine cream and milk and heat to simmer. Add chocolate and stir to melt. Whisk together sugar, egg yolks and whole eggs. Whisk in the milk mixture. Add vanilla. Pour some of the bread slices and let it soak in about 10 minutes. Then add the remainder. This can be held in the refrigerator for a few hours before baking.
When you are ready, bake covered at 300°F for one hour. Remove cover, reduce the oven temperature to 275°F and bake until a knife inserted into the custard comes out clean. Depending on the oven, it could take another hour or more.
While pudding is baking, in a sauce pan over medium heat, melt butter and add brown sugar. Cook for 5-6 minutes until sugar granules are incorporated into the butter.
Now add corn syrup and rum. Simmer for 5 minutes to allow alcohol to burn off, then serve.
