Break bread into small pieces into an 8 inch square baking pan. Drizzle melted butter over bread. If desired, sprinkle with raisins.
In a medium mixing bowl, combine eggs, 2 cups whipping cream, sugar, 1/4 cup brown sugar, cinnamon, and vanilla. Beat until well mixed. Pour over bread, and lightly push down with a fork until bread is covered and soaking up the egg mixture.
Bake in the preheated oven for 45 minutes, or until the top springs back when lightly tapped.
While this is baking, stir remaining brown sugar and butter in heavy medium saucepan over medium heat until melted and smooth, about 2 minutes. Add cream, rum, and cinnamon and bring to simmer. Simmer until sauce thickens and is reduced to 1 1/2 cups, about 5 minutes. Serve warm. (Can be prepared 2 days ahead. Cover and refrigerate. Bring to simmer before serving.)