Preheat oven to 350 degrees.
Place the bread pieces in a large bowl.
In a separate bowl, whisk the heavy cream, milk, both sugars, eggs and the vanilla until well combined.
Pour the mixture over the bread and let it sit for about 10 minutes, or until the bread soaks up all the mixture.
Coat the bottom of an 8-inch square baking pan with the melted butter making sure to cover the sides of the pan as well.
Spoon the bread mixture into the pan and spread into a single layer.
Place it in the oven and bake for about about 35 - 40 minutes, or until the bread pudding has set and edges are golden brown. Remove from the oven and let it cool on a wire rack.
To make the dulce de leche sauce: Place dulce de leche on a small bowl and warm in the microwave for about 30 seconds. Add milk and mix well, until smooth. Stir in more milk if necessary to thin it out until you achieve the desired consistency.
Drizzle half of the dulce the leche over the bread pudding. Cut the bread pudding into squares to serve. Drizzle a bit more dulce de leche if you’d like and top with vanilla ice cream, if desired.