Generously butter a 9- by 13-inch baking dish (or any 3.5–4-quart) or spray with nonstick spray.
Whisk brown sugar, cinnamon, nutmeg, and salt in a bowl. Set aside.
Sprinkle 3 tablespoons of brown sugar mixture evenly over the bottom of the prepared dish.
Place 6 bread slices (use bread heels here) in an even layer in bottom of dish. You may need to slice the bread into smaller pieces to create an even layer of bread. Brush bread with 2 tablespoons melted butter and sprinkle with 3 tablespoons sugar mixture.
Place 6 bread slices in single layer over first layer, brush with 2 tablespoons melted butter, then sprinkle with 3 tablespoons sugar mixture.
Place remaining 6 bread slices over previous layer and brush with 2 tablespoons melted butter.
In a separate bowl, whisk eggs, milk, and vanilla together until well combined. Pour milk mixture over bread. Cover the pan tightly with plastic wrap and refrigerate for 12 hours.
Preheat oven to 350°F (177°C). Remove the pan from the refrigerator. Sprinkle the top of the bread with the remaining heaping 3 tablespoons of brown sugar mixture.
Bake until the custard is set, puffed up, and reaches an internal temperature in the center of 175 to 190ºF (79 to 88ºC), about 45 to 50 minutes. If the bread starts to brown too quickly, loosely cover the top with foil after about 45 minutes of baking.
Transfer the casserole to a wire rack and let it cool for 15 minutes. Casserole deflates slightly as it cools.
Serve warm with powdered sugar, a drizzle of maple syrup, and fresh berries if desired.