Preheat the oven to 325°F and line a 9x9-inch pan with parchment, leaving overhang on two sides.
Combine the graham cracker crumbs, melted butter, and 3 tablespoons sugar. Press firmly into the pan and bake for 8 minutes. Set aside.
Beat the cream cheese and ¾ cup sugar together until smooth, about 2 minutes.
Beat in the eggs one at a time, then the eggnog, vanilla, and nutmeg, mixing just until smooth.
Pour the filling over the crust and smooth the top.
Bake for 32–35 minutes, until the edges are set and the center has a slight jiggle.
Cool in the pan for 30 minutes, then refrigerate for at least 4 hours before lifting out and slicing into 16 bars.
Dust with a little extra nutmeg just before serving.