Pour the apple cider into a saucepan and simmer until reduced to 1 cup. Set it aside to cool while preparing the pan and batter.
Preheat the oven to 350°F or 175°C. Grease and flour a 10-cup Bundt pan thoroughly, reaching every curve and center edge.
Whisk flour, baking powder, baking soda, cinnamon, and salt. In another bowl, beat softened butter with both sugars until creamy.
Add the eggs one at a time, followed by vanilla and sour cream. Mix in the dry ingredients alternately with the cooled cider, beginning and ending with flour.
Pour the batter into the pan and smooth the surface. Bake for 40 to 48 minutes, until a tester comes out clean.
Cool for 15 minutes, then invert onto a rack. Brush the warm cake with melted butter and sprinkle the cinnamon-sugar mixture over every side.
