Preheat the oven to 350F degrees.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg,and salt. In a separate large bowl, whisk together the apple cider, apple sauce, brown sugar, white sugar, olive oil, eggs, and vanilla. Add in the shredded apple and stir to combine.
Then add the apple cider mixture to the flour mixture. Stir until just combined, do not overmix. Grease and flour a standard size Bundt pan, or use a spray that has flour included - otherwise, the cake will not remove easily. Pour the batter into the prepared pan.
Bake at 350 degrees for 50 minutes. The top should bounceback when lightly pressed. Allow the cake to cool in the pan for 15 minutes, then remove from the pan.
Mix together the ¼ cup sugar and 1 teaspoon ground cinnamon to create cinnamon sugar. Brush the cake with melted butter and sprinkle on the cinnamon-sugar mixture. You may need to press the cinnamon-sugar on to the cake to help it stick on the sides.
Optional: If you would like to add a glaze to your cake, just whisk together powdered sugar and apple cider, and pour over your cake or use it as a dipping sauce. For a thicker sauce, use less cider, for a thinner sauce use more.