Preheat your oven to 350°F (175°C). Butter a 9x13-inch baking dish generously and set aside.
Spread the bread cubes in the prepared baking dish in an even layer. Tuck the peach slices throughout the bread, distributing them evenly.
In a large mixing bowl, whisk together the eggs, milk, heavy cream, brown sugar, granulated sugar, vanilla extract, cinnamon, nutmeg, and salt until the sugars dissolve and the mixture is smooth.
Pour the melted butter over the bread and peaches, then slowly pour the custard mixture over everything, pressing down gently with a spatula to help the bread absorb the liquid. Let stand for 10 minutes.
Sprinkle the turbinado sugar evenly over the top. Cover loosely with aluminum foil.
Bake covered for 30 minutes, then remove the foil and continue baking for 20-25 minutes until the top is golden brown and the center barely jiggles when gently shaken.
Remove from the oven and let rest for 15 minutes before serving. The pudding will continue to set as it cools slightly, making it easier to slice while staying custardy inside.