Preheat the oven to 350. Line a jelly roll pan (the shallow ones that are 10 by 15) with foil, spray the foil (make sure you get the sides) with cooking spray and lightly dust it with flour.
Beat the eggs on high until frothy, about five minutes.
Beat in the sugar, oil, and vanilla.
In a separate bowl, whisk together your dry ingredients, the flour, salt, baking powder and spices, until combined. Now add them to your wet ingredients by folding them in. Do not over mix.
Pour the batter into your jelly roll pan. Gently move it over the pan to spread it evenly.
Bake for about 9 minutes.
While the cake is baking spread a clean towel on the counter, sprinkle very liberally with powdered sugar making sure that no area of the towel that will see cake is showing.
As soon as the cake comes out of the oven, flip it over onto the towel and peel away the tin foil carefully. Roll the cake up in the towel.
Let the cake cool, rolled up in the towel, for at least an hour, but not longer than four hours.
While the cake is cooling,make the frosting, beat the butter until fluffy. Then add the powdered sugar gradually, one cup at a time. Finally, add the rum and the eggnog.
After the cake has finished cooling, unroll it. Gently frost the cake, making sure to cover the whole thing, though the thicker you add the frosting the more likely it will be to crack when you roll it back up.
Roll the cake back up. Whisk together the powdered sugar and eggnog. Pour over the cake, sprinkle with ground cinnamon. Allow the glaze to set before slicing and serving.
