Preheat oven to 350°F. Prepare a 9x13 baking dish by greasing with butter and set aside.
In a large bowl, whisk eggs, egg nog, brown sugar, vanilla extract, salt, and nutmeg until combined.
Dip both sides of each slice of bread into the egg nog mixture, then place in pan at a slight angle, leaning the first slice against one wall of the pan. Repeat with remaining slices of brioche, laying them against one another at an angle, so they are neither completely flat nor standing straight. Pour any remaining egg nog mixture over the slices of brioche.
Bake for 35-40 minutes, until the egg nog mixture is cooked and the tops of the brioche is golden.
Remove from oven and serve with maple syrup, whipped cream, and a sprinkle of nutmeg.
