Adjust the oven rack to the lower middle position and preheat to 350°F. Generously grease and flour a 10 or 12-cup Bundt pan.
In a medium bowl whisk together the flour, cinnamon, salt, baking soda, and baking powder. Set aside.
In a large mixing bowl combine the melted cooled butter, eggs, sugars, applesauce, vanilla and ⅔ cup of the reduced cider. Add the flour mixture and blend with a spatula until mostly smooth with a few small lumps, taking care not to overmix.
Pour the batter into the prepared pan and bake for 45 - 55 minutes or until a toothpick inserted in the center comes out with no wet batter. Moist crumbs are fine. Cool the cake in the pan for 15 minutes.
Mix together the remaining 2 teaspoons ground cinnamon and ⅓ cup granulated sugar for the topping.
Invert the warm cake onto a wire rack set over a rimmed baking sheet lined with parchment paper. Brush the cake all over with the remaining cider and coat immediately with the cinnamon sugar mixture. Cool before serving or the cake will be crumbly.
Store the cake covered, at room temperature, for up to 2 days or refrigerate for longer storage.