Preheat the oven to 350 degrees and grease a 9x9 baking dish with the butter.
In a large bowl, whisk together the eggs, milk, brown sugar, cinnamon, and vanilla until smooth.
Add the bread cubes and diced apples to the bowl. Stir gently until everything is coated.
Pour the mixture into the prepared baking dish and spread it evenly.
Bake for 35 to 40 minutes until the top is golden and the center is set.
Remove from the oven and let it rest for 5 minutes before serving with maple syrup.