Old-fashioned vanilla custard pudding

Ingredients :

For the bread pudding:

6 cups of one-day bread cubed (white or brioche)
4 large eggs
2 cups of milk
1 cup of heavy cream
3⁄4 cup of granulated sugar
1 teaspoon of vanilla extract
1 teaspoon ground cinnamon
1⁄2 teaspoon ground nutmeg
1⁄2 cup raisins or cranberries (optional)
2 tablespoons of unsalted butter, melted
For the vanilla sauce:

1 cup of powdered sugar
1⁄2 cup unsalted butter, softened
1 teaspoon of vanilla extract
2-4 tablespoons of milk (adjust for desired consistency)
Instructions :

Prepare the bread pudding:

Preheat your oven to 350°F (175°C). Greasing a 9×13 inch plate.
In a large bowl, combine cubed bread and melted butter. Toss to coat and place the mixture in the prepared dish.
In another bowl, whisk together eggs, milk, heavy cream, granulated sugar, vanilla extract, cinnamon, nutmeg and raisins (if using).
Pour the egg mixture over the bread cubes, pressing gently to ensure all the bread is moist. Let it rest for about 10-15 minutes.
Make the bread pudding:

Bake in a preheated oven for 45-50 minutes, or until the top is golden brown and a toothpaste inserted in the center comes out clean.
Prepare the vanilla sauce:

In a mixing bowl, beat together the soft butter and powdered sugar until smooth.
Stir in the vanilla extract and add the milk, one tablespoon at a time, until you reach the consistency of your vanilla.