Pour 2 cups of apple cider into a small saucepan and bring to a gentle boil over medium heat. Simmer, stirring occasionally, until reduced to about ½ cup of thick liquid (15–20 minutes). Remove from heat and cool to room temperature.
Preheat oven to 350°F. Grease a 9x5 inch loaf pan and line with parchment paper, leaving overhang on the long sides.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt until evenly distributed.
In a large bowl, whisk oil, granulated sugar, and brown sugar until combined. Add eggs one at a time, whisking well after each. Whisk in sour cream, vanilla, and cooled reduced apple cider until smooth and glossy.
Add dry ingredients to wet ingredients and fold gently with a spatula just until no streaks of flour remain. A few lumps are fine. Do not overmix.
Pour batter into the prepared pan and smooth the top. Bake on the center rack for 50–60 minutes, until a toothpick inserted in the center comes out clean. Tent with foil during the last 15 minutes if browning too quickly.
Cool in the pan on a wire rack for 15 minutes. Then lift out using the parchment overhang and transfer directly to the rack to finish cooling.
While still warm, brush melted butter over the top and sides. In a small bowl, mix ¼ cup sugar and 1 tablespoon cinnamon, then sprinkle evenly over the buttered loaf, pressing lightly. Cool for 30 minutes before slicing.