Preheat oven to 350 degrees F. Butter an 8-inch or 9-inch square baking pan, then line with parchment paper; set aside.
Stir together the graham cracker crumbs, 3 tablespoons of granulated sugar, and the melted butter. Press into the bottom of the prepared pan. Bake until the crust is just brown around the edges, 12 to 15 minutes. Let cool.
Meanwhile, beat the cream cheese with a mixer on medium speed until fluffy, about 2 minutes. Add the remaining ¾ cup granulated sugar and beat for an additional couple of minutes, until smooth. Add the eggs and yolk, eggnog, brandy and vanilla and beat again until completely combined and smooth. Finally, beat in the flour, nutmeg and salt and mix until smooth.
Pour the filling over the crust. Set the pan in a larger pan (a 9x13-inch works for this), and add enough hot water to come halfway up the sides of the baking pan. Bake until just set, 40 to 45 minutes. Remove the baking pan from the water bath, and transfer to a wire rack. Let cool for 30 minutes, then refrigerate for at least 3 hours or overnight.
Cut into 1½x3-inch bars. Lightly dust the tops of the bars with freshly grated nutmeg just before serving. Store leftovers in an airtight container in the refrigerator.
Note: If you don't wish to use the brandy, you can simply omit it.