Place a rack in middle of oven; preheat to 325°. Lightly butter an 8½x4½” or 9×5″ loaf pan. Line with parchment paper, leaving overhang on both long sides. Bring cider to a boil in a medium saucepan over medium-high heat. Reduce heat and simmer until cider is reduced to ¾ cup, 8–10 minutes. Pour ¼ cup reduced cider into a small measuring glass or bowl and set aside. Transfer remaining reduced cider to a small bowl and let cool 5 minutes. Stir in sour cream and vanilla and set aside.
Melt 8 Tbsp. butter in same saucepan (no need to clean) over low heat. Let cool slightly. Whisk flour, cornstarch, baking powder, baking soda, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, ½ tsp. cinnamon, and ¼ tsp. nutmeg in a medium bowl to combine.
Vigorously whisk eggs and ¾ cup (150 g) sugar in a large bowl until pale, voluminous, and frothy, about 2 minutes. Whisking constantly, gradually add melted butter in a steady stream; continue to whisk until fully combined and emulsified (no spots of fat should remain). Reserve saucepan.
Whisk dry ingredients into egg mixture in 3 additions, alternating with reserved sour cream mixture in 2 additions; whisk just until no lumps remain. Batter will be thin.
Scrape into pan and set on a rimmed baking sheet. Bake cake, rotating halfway through, until deep golden brown and a tester inserted into the center comes out clean, 60–80 minutes. Transfer pan to a wire rack and poke top of cake all over with a toothpick. Spoon 3 Tbsp. reserved reduced cider over; let cool 10 minutes.
Meanwhile, mix a big pinch of salt, remaining ¼ cup (50 g) sugar, ½ tsp. cinnamon, and ¼ tsp. nutmeg in a small bowl. Melt remaining 1 Tbsp. butter in reserved saucepan and mix into remaining 1 Tbsp. reduced cider.
Using parchment paper, lift cake onto rack and set rack inside rimmed baking sheet. Peel away parchment from sides. Brush warm butter mixture over top and sides of cake. Sprinkle generously with sugar mixture to coat every surface (use parchment to help rotate cake and collect any excess sugar). Remove parchment and let cool completely before slicing.
Do ahead: Cake can be made 4 days ahead. Store tightly wrapped at room temperature.