In a small saucepan, simmer the apple cider over medium heat until it reduces to about 3/4 cup, about 15 to 20 minutes. Let it cool before adding it to the batter.
Preheat the oven to 350°F. Grease a Bundt pan very well.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla and cooled apple cider reduction.
In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Add the dry ingredients to the wet ingredients in batches, alternating with the sour cream or Greek yogurt. Mix just until combined.
Pour the batter into the prepared pan and smooth the top. Bake for 35 to 45 minutes, or until a toothpick inserted near the center comes out clean.
Let the cake cool in the pan for 15 minutes, then carefully turn it out onto a cooling rack.
While the cake is still warm, brush it with melted butter. Stir together the granulated sugar and cinnamon, then sprinkle it over the buttered cake.