Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or non-stick spray.
Slice the bread into 1-inch thick pieces and spread them evenly across the bottom of the baking dish, creating a sturdy layer.
Peel, core, and thinly slice the apples, then scatter them over the bread layers, distributing them evenly for consistent bites.
In a large mixing bowl, whisk together the eggs, milk, brown sugar, cinnamon, nutmeg (if using), and vanilla until the mixture is smooth and fragrant.
Slowly pour the custard mixture over the bread and apple layers, ensuring each piece is soaked evenly. Gently press down on the bread to help it absorb the liquid.
Drizzle the melted butter evenly over the top of the layered dish for a golden, crisp finish during baking.
Place the baking dish in the preheated oven and bake for 40 to 45 minutes, or until the top is golden brown and bubbling around the edges.
Remove the bake from the oven and let it cool for a few minutes. The casserole should be set with a slightly crispy top and a moist, custardy interior filled with tender apples.
Slice into portions and serve warm, optionally with a drizzle of maple syrup or a sprinkle of powdered sugar for extra sweetness.