In a wide, shallow bowl (large enough to hold your bread), whisk together the eggs, eggnog, and nutmeg until combined. Set aside.
Layer the sandwich any way you like: I prefer to spread a small amount of mayonnaise on each piece of bread, then layer cheese on each side, and finish with ham and bacon. Then flip one side onto the other.
Dip the sandwich into the egg-eggnog mixture, making sure to coat it evenly on all sides.
Heat a nonstick pan over medium-high heat. Add the butter and wait for it to melt. Once the butter has melted, add the sandwich and cook for 1-2 minutes per side, or until the edges are golden brown and the cheese has melted.
Serve the sandwich immediately with the eggnog-cranberry syrup and eggnog whipped cream.