Reduce the cider. Pour the 1 1/2 cups of apple cider into a small saucepan and bring it to a simmer over medium heat. Simmer gently for about 20 minutes, until it has reduced to 3/4 cup. Set aside to cool while you prepare the pan and batter.
Heat the oven and prepare the pan. Heat the oven to 350°F. Grease a 9x5-inch loaf pan and line it with parchment paper, leaving an overhang on the two long sides for lifting. While the cider cools, measure out the remaining ingredients — about 10 minutes of measuring and mixing in all.
Whisk the dry ingredients. In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt until evenly combined.
Cream the butter and sugars. In a large bowl, beat the softened butter, granulated sugar, and brown sugar together for about 2 minutes, until light and fluffy. Beat in the eggs one at a time, then the vanilla.
Add the wet ingredients. Stir in the sour cream and the cooled 3/4 cup of reduced cider until the mixture is smooth. It may look slightly curdled at this point; that smooths out once the flour goes in.
Finish the batter. Add the dry ingredients to the wet ingredients in two additions, stirring just until no dry flour remains. Fold in the diced apple. Do not overmix, or the loaf turns tough.
Bake. Scrape the batter into the prepared pan and smooth the top. Bake for about 60 minutes, until a toothpick inserted in the center comes out with a few moist crumbs and the center reads 200°F to 205°F on an instant-read thermometer. If the top browns too fast, tent it loosely with foil for the last 15 minutes.
Cool in the pan. Let the loaf cool in the pan for 15 minutes, then lift it out by the parchment and set it on a wire rack.
Coat while warm. While the loaf is still warm, brush all sides with the melted butter, then roll it gently in the cinnamon sugar, pressing lightly so the coating sticks. Let it cool to lukewarm before slicing into 10 slices.
