The night before you plan to serve the dish, whisk together the eggs, eggnog, cinnamon, nutmeg, salt, and vanilla in a large mixing bowl. Add the bread cubes and toss until the bread is coated.
Pour ¼ cup melted butter into the bottom of a 9 by 12 inch baking dish and swirl to coat the bottom of the dish with butter. Pour in the bread mixture. Cover with plastic wrap and refrigerate overnight.
In the morning, remove the dish from the fridge and let sit at room temperature while the oven preheats. Preheat oven to 350 degrees.
Drizzle the remaining ¼ cup melted butter over the top, sprinkle on the brown sugar and bake, uncovered for 45 minutes. Let sit a few minutes before serving. This dish can also be fully baked, cooled, and refrigerated and then reheated before serving.