In a large shallow-bottom bowl, whisk together the eggs.
Whisk in the eggnog, melted butter, vanilla extract, rum extract, ground nutmeg and ground cinnamon. If your butter forms clumps, it's ok - it'll melt when you fry the French toast.
Heat an electric griddle to 350F degrees, or heat a large frying pan to medium heat. Drizzle with oil or spray with non-stick cooking spray.
Submerge a piece of bread in the batter, then flip and submerge the other side. Shake off any extra batter and place on the heated griddle or frying pan. Fry on one side until golden (about 2-3 minutes), then flip to the other side and continue frying until golden. Repeat with the process with all of the bread.
Serve warm with maple syrup, whipped cream and a sprinkle of nutmeg.
Serve immediately. Leftovers can be stored in a ziploc bag in the fridge for up to 2 days. Reheat on a plate in the microwave.