Start by preheating your oven to 350°F. Grease an 8- or 9-inch square or round baking dish and set it aside.
Core and cube the apples. Cut your day-old bread into even cubes.
In a large mixing bowl, whisk together the eggs, whole milk, brown sugar, granulated sugar, maple syrup, cinnamon, and nutmeg until fully combined.
Add the bread cubes and cubed apples to the wet mixture. Stir everything together until the bread is fully moistened.
Pour the mixture into your prepared baking dish. Place it in the oven and bake for 45-50 minutes. If you notice the top browning too quickly, cover it with a piece of aluminum foil.
The pudding is ready when it's set and golden brown on top. You can use a toothpick to check: if it comes out clean or with just a few crumbs, your pudding is done.
Let the pudding cool for a few minutes, then serve it warm. Add toppings of your choice, like vanilla ice cream or caramel sauce.