Place the torn French bread in a large mixing bowl.

Pour the whole milk over the bread and let it soak for at least 1 hour, stirring once or twice.

Preheat the oven to 350°F.

In a separate bowl, whisk together the eggs, granulated sugar, and vanilla extract until smooth.

Pour the egg mixture into the soaked bread and stir until evenly combined. Fold in the raisins if using.

Place the 3 tablespoons butter in a 9x13-inch baking dish and warm it briefly in the oven until melted.

Carefully swirl the melted butter over the bottom and sides of the dish.

Pour the bread pudding mixture into the prepared baking dish.

Bake for about 1 hour, until the top is golden and the center is set.

Let the bread pudding rest for 15–20 minutes before cutting into squares.

For the sauce, combine the sugar, butter, beaten egg, and apple juice or milk in a saucepan over low heat.

Cook while stirring constantly until the sugar dissolves and the sauce becomes smooth and glossy. Do not let it boil rapidly.

Remove the sauce from the heat and stir in the vanilla extract.

Spoon the warm sauce over each serving of bread pudding.