Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, baking powder, salt, nutmeg, and cinnamon until well combined.
Add the cold cubed butter to the flour mixture. Using a pastry cutter or your fingertips, work the butter into the flour until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the eggnog, egg, and vanilla extract until well blended.
Pour the wet ingredients into the dry ingredients, and gently mix until just combined, being careful not to overwork the dough.
Turn the dough out onto a lightly floured surface and gently knead it a couple of times until it holds together. Pat it into a rectangle about 1-inch thick.
Cut into triangles or circles using a sharp knife or a biscuit cutter, and place them on the prepared baking sheet.
Bake in the preheated oven for 15-18 minutes or until the tops are lightly golden.
While the scones are baking, prepare the nutmeg glaze. In a small bowl, combine the powdered sugar and milk, adding just enough milk to achieve a smooth, pourable consistency.
Once the scones are done, let them cool slightly on a wire rack. Drizzle the nutmeg glaze over the warm scones and sprinkle with extra nutmeg for a festive touch.