For the cake: Preheat the oven to 350˚F. Lightly spray a springform pan with cooking spray.
In a medium bowl, beat together the eggs, eggnog, brandy extract, oil, white sugar, vanilla and butter together.
In a separate bowl, mix together the flours, baking powder, salt and nutmeg until fully combined. Mix in the wet ingredients and mix until fully incorporated.
Pour the mixture into the prepared pan and bake for 40-60 minutes, or until a toothpick inserted comes out clean. Let cool in pan for 10 minutes, then remove to cool on wire racks.
For the glaze: In a medium bowl, mix together all the glaze ingredients, adding more eggnog until the glaze reaches your desired consistancy.