In a large mixing bowl, sift flour, sugar, cinnamon, baking powder, baking soda, and salt together.
Add chocolate chips.
Add the butter and cut it in until the butter is in small pieces. Create a well in the dry ingredients and add the eggnog, egg, and extract in the middle. Gently stir until combined.
Place dough onto a prepared pan. Shape the dough into an 8-inch circle. Use a sharp knife to score into 8 sections. Bake at 400 for 20 minutes. Remove for the oven and cut scones through the scored sections. Let cool.
Frosting
Stir together the powdered sugar and water. Spoon into a plastic bag with a corner cut off. Drizzle over the scones.