Preheat oven to 375F and line a sheet pan with parchment paper. Sprinkle the parchment paper with a bit of flour and set aside.
Whisk together dry ingredients in a mixing bowl.
Add the butter to the same bowl, mixing in with clean hands or a pastry cutter. Stir in the chocolate chips.
Whisk the milk with the egg and vanilla, then slowly incorporate into the dry ingredients. Stir until just combined.
Turn out dough onto parchment paper sprinkled with flour. Shape into a flattened circle. Using a knife, cut the dough wedges.
Bake 15-20 minutes or until golden brown on top. Let cool 10 minutes.
Meanwhile, whisk the eggnog, powdered sugar and a pinch of nutmeg together to form a glaze. Add more powdered sugar or eggnog to adjust the consistency to your liking. Drizzle on top and serve!