Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish with the melted butter. Spread the cubed stale bread evenly in the prepared dish.
In a large bowl, whisk together the eggs, milk, heavy cream, sugar, vanilla extract, cinnamon, nutmeg, and salt until well combined.
Pour the custard mixture evenly over the bread cubes, making sure all the bread is moistened. Gently press down on the bread to help it soak up the custard. Let it sit for about 20-30 minutes to allow the bread to absorb the liquid.
Place the baking dish in the preheated oven and bake for 45-50 minutes, or until the bread pudding is golden brown and the custard is set. A knife inserted into the center should come out clean.
While the bread pudding is baking, make the vanilla sauce. In a medium saucepan, combine the heavy cream, sugar, butter, and salt. Cook over medium heat, stirring constantly, until the sugar is dissolved and the butter is melted. Bring the mixture to a simmer and let it cook for 2-3 minutes, stirring occasionally, until slightly thickened. Remove from heat and stir in the vanilla extract.
Let the Classic Bread Pudding with Vanilla Sauce cool slightly before serving. Drizzle generously with the warm vanilla sauce.