Preheat your oven to 325 degrees F. Spray a bundt pan with non-stick spray and then dust with flour. Set aside.
In a medium size mixing bowl, combine the flour, cinnamon, nutmeg, salt, and baking powder. Whisk to combine. Set aside.
In a large bowl, combine the sugar, brown sugar and oil. Mix on medium speed to combine.
Add the eggs to the sugar mixture and mix on medium speed for about two minutes.
Add the applesauce and vanilla. Mix to combine.
With the mixer on low speed, add 1/3 of the flour mixture, followed by half of the apple cider. Continue alternating the flour mixture and the apple cider, finishing with the flour mixture. Mix until no streaks of flour remain. The batter will be slightly thin, not thick.
Pour the batter into the bundt pan and bake for 50 minutes. The cake is done when a toothpick inserted in the center of the cake comes out with a few moist crumbs on it.
Let the cake cool for an hour in the bundt pan before turning it over onto a cake plate or cooling rack.
Using a pastry brush, coat the cake in butter.
Combine the 1/4 cup sugar and 2 teaspoons cinnamon and then sprinkle onto the top and sides of the cake. To coat the sides, it's best to fill your hand with the mixture and pat it on the cake.