Bring the apple cider to a simmer in a small saucepan over medium heat and cook for 15 to 20 minutes, until reduced to 1 cup.

Transfer the reduced cider to a measuring cup and cool completely.

Heat the oven to 350°F.

Thoroughly grease and flour a 10- to 12-cup Bundt pan.

Whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg in a medium bowl.

Beat the softened unsalted butter, granulated sugar, and packed light brown sugar in a large bowl with an electric mixer on medium speed for 3 to 4 minutes, until light and fluffy.

Beat in the eggs one at a time, then beat in the vanilla extract.

Whisk the sour cream into the cooled cider, then add this mixture to the butter mixture in three additions, alternating with the flour mixture in two additions; begin and end with the flour mixture, mixing on low just until combined.

Spoon the batter into the prepared pan and smooth the top, then bake for 50 to 60 minutes, until a toothpick inserted in the center comes out with a few moist crumbs.

Cool the cake in the pan for 10 minutes, then invert it onto a wire rack and lift off the pan; cool for about 20 minutes, until warm but not hot.

Stir together the granulated sugar and ground cinnamon in a small bowl.

Brush the melted unsalted butter over the warm cake, then sprinkle the cinnamon sugar over the top and sides, pressing gently so it adheres.