Peach bread pudding with caramel sauce

2 cups fresh peaches - peeled, pitted and halved
1 (14 ounce) can sweetened condensed milk
3 eggs, lightly beaten
1 1/4 cups hot water
1/4 cup butter, melted
1 teaspoon ground cinnamon
1 teaspoon vanilla extract
4 cups French bread, torn into small pieces

CARAMEL SAUCE
1/2 cup brown sugar
1/2 cup butter
2 tablespoons light corn syrup
1 tablespoon rum
If you prefer, you can omit the rum and use 2
teaspoons of vanilla extract in the caramel sauce
instead.

Directions:
Preheat an oven to 325 degrees F (165 degrees C).
Grease a 9x13-inch baking dish.
Chop the peaches and lightly mash them in a
mixing bowl. Combine the sweetened condensed
milk and the eggs; add them to the peaches and
mix well. Stir in the hot water, melted butter,
cinnamon, and vanilla. Stir the French bread into to
the custard mixture until the bread is completely
moistened. Turn the pudding into the prepared
baking dish.
Bake until a knife inserted in the center of the
pudding comes out clean, about 1 hour and 10
minutes.
While the pudding is baking, combine the brown
sugar, 1/2 cup butter, corn syrup, and rum in a
saucepan. Bring to a boil over medium heat and
simmer for 3 to 4 minutes or until just slightly
thickened. Let cool slightly.
Remove the pudding from the oven and let it cool for
about ten minutes before serving. Serve warm with
the caramel sauce. Cool and cover any leftover
pudding and store it in the refrigerator.