Preheat oven to 350°F. Grease and flour a Bundt pan.
In a saucepan, simmer apple cider over medium heat until reduced to ¾ cup. Let cool.
In a large bowl, cream butter, granulated sugar, and brown sugar until fluffy.
Add eggs, one at a time, beating well after each addition. Mix in vanilla and sour cream.
In another bowl, whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Gradually add dry ingredients to the wet ingredients, alternating with the reduced cider.
Pour batter into the prepared pan and bake for 40–45 minutes or until a toothpick comes out clean.
Cool in the pan for 10 minutes, then invert onto a wire rack to cool completely.
Brush the cooled cake with melted butter and sprinkle with the cinnamon-sugar topping.