In a saucepan, heat cream, milk, condensed milk, and vanilla bean seeds until hot.
Remove from heat and stir in 2½ cups of white chocolate until melted.
In a bowl, whisk eggs and yolks. Slowly add warm cream mixture while whisking constantly.
Pour custard over sliced bread and let soak for 20 minutes.
Stir in remaining white chocolate chunks.
Transfer to a greased 9×13-inch baking dish. Cover with foil and bake at 350°F for 1 hour.
Remove foil and bake an additional hour until golden and set.
Let cool before slicing. Drizzle with rum caramel sauce to serve.