Grease a 9-inch x 13-inch baking dish with butter. Place the bread cubes into the pan. Sprinkle the raisins over the bread and drizzle the melted butter all over without mixing the bread cubes. Set aside.

In a large mixing bowl, whisk the eggs until evenly beaten. Then whisk in the sugars, half-and-half, milk, and vanilla until well combined. Pour the egg mixture over the bread cubes and gently press the bread down into the custard. Let it rest for at least 1 hour.

Preheat the oven to 350 degrees F. Bake the bread pudding uncovered for 35 minutes. Then loosely cover the dish with foil and bake for another 10 minutes.

While the bread pudding is baking, make the sauce. In a medium saucepan over medium heat, add the butter and brown sugar, stirring constantly until melted. Whisk in the evaporated milk and bring to a boil, again stirring constantly. Remove from heat and whisk in the vanilla and salt. Set aside.

Remove the bread pudding from the oven, take off the foil, and allow it to cool for about 10 minutes before serving. Cut into slices, pour the vanilla caramel sauce over each slice, and serve warm.