Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large bowl, combine the cubed bread and diced peaches. Toss gently to mix.
In another bowl, whisk together the milk, heavy cream, eggs, granulated sugar, vanilla extract, cinnamon, and salt until well combined.
Pour the egg mixture over the bread and peaches, making sure all the bread is soaked. Let it sit for about 15 minutes to absorb the liquid.
Drizzle the melted butter over the mixture and sprinkle the brown sugar and nutmeg (if using) on top.
Bake in the preheated oven for 45-50 minutes, or until the top is golden brown and the pudding is set.
Remove from the oven and let it cool for about 10 minutes before serving.