Preheat oven to 325°F. Spray a 9x5 loaf pan and line with a sheet of parchment paper so you can more easily lift the bread out after baking. (This is optional.)
Put the cider in a small saucepan and bring to a boil. Boil for about 10 minutes, or until the liquid is reduced to 1/2 cup.
Pour the cider into a small bowl and set aside to cool slightly. Then stir in the sour cream and vanilla.
Melt the butter in the same saucepan. Let cool slightly.
Meanwhile beat the eggs and brown sugar until smooth and frothy. I do this in my stand mixer but you can also do this with a whisk.
Drizzle the melted butter into the egg mixture, while the machine is running on low. If doing by hand, keep whisking while you add the butter to get everything incorporated.
In a separate bowl, whisk together the flour, cornstarch, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
Add the dry ingredients to the egg mixture, alternately with the cider/sour cream mixture, beginning and ending with the dry ingredients. Mix just until combined but don't over mix.
Pour the batter into your prepared pan and bake for about 55 minutes, or until a toothpick inserted in the center comes out without we batter on it. Note: if you use a slightly smaller loaf pan your cake may take longer to bake.
Let the pan cool on a rack for ten minutes, then remove the cake from the pan using the parchment paper sling. Let cool for 5 more minutes.
For the sugar coating, mix the sugar with the cinnamon. Brush the outside of the cake with melted butter and coat thickly with the cinnamon sugar. I do the top first, then each side, one at a time. For the sides I cup the sugar in my hand and quickly press up against the cake. Do this a few times until you get the surface well covered.
Do not slice the cake until ready to enjoy. Store at room temperature loosely covered with foil.
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Notes
The low 325F oven temperature encourages this cake to cook slowly and evenly, making for a nice soft texture. Be sure your oven is accurate! I recommend an inexpensive oven thermometer so you can know for sure.Boiling down the cider thickens it and concentrates the flavor. You can also use a ready-made boiled cider like this one.Be sure to pat on your cinnamon sugar crust nice and thickly, it's a big part of the charm of this apple cider doughnut cake.