Preheat the oven to 350°F.
Place the challah cubes in a 9 x 13-inch baking pan. Pour the beer over the cubes and toss to coat. Let sit 15 minutes. Place the eggs, sugar, vanilla and milk in a medium bowl and whisk until combined. Pour or ladle over the beer-soaked challah and bake for 50 minutes, or until the pudding is set and the edges browned.
Meanwhile, make the Caramel Sauce. Place the sugar in a heavy-bottomed saucepan over medium heat and cook, stirring often, until all of the sugar has melted and you have a deep amber-colored syrup. Remove from the heat and carefully add the boiling water. The mixture will boil up and you will see some balls of caramel in the pot. Return the pan to medium heat and cook at a rolling boil for 10 minutes. Stir often until all of the caramel pieces have melted and you have a smooth syrup. Let cool, cover with plastic, and store at room temperature.
To serve, cut the pudding into squares, place on your serving plate and drizzle on the Caramel Syrup. Serve warm or at room temperature. The pudding can be reheated in a warm oven (200°F) for 20 minutes.