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Preheat the oven to 350 degrees. Grease and flour a standard size Bundt pan. (Or use a spray that has flour included - otherwise, the cake will not remove easily.)
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In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
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In a separate large bowl, whisk together the apple cider, apple sauce, brown sugar, white sugar, olive oil, eggs, and vanilla. Add, then stir in the shredded apple.
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Then add the apple cider mixture to the flour mixture. Stir until just combined. (When you don’t see any more flour, stop - do not overmix). Pour the batter into the prepared pan.
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Bake at 350 degrees for 50 minutes. The top should bounce back when lightly pressed.
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Allow the cake to cool in the pan for 20 minutes, then remove from the pan.
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Mix together the ¼ cup sugar and 1 teaspoon ground cinnamon to create cinnamon sugar.
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Brush the cake with melted butter and sprinkle on the cinnamon-sugar mixture. You may need to press the cinnamon-sugar onto the cake to help it stick on the sides.
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If you would like to add a glaze to your cake, just whisk together 2 cups of powdered and 3 tablespoons of cider (add more cider a tablespoon at a time depending on if you want a thinner glaze) and pour over your cake or use it as a dipping sauce.