Heat the Oven & Prep the Pan: Heat the oven to 325°F (163°C) and place a rack in the middle. Grease or butter an 8½ x 4½-inch loaf pan and line it with parchment paper, leaving extra on the sides to use as handles.
Reduce the Apple Cider: In a medium saucepan, bring 1½ cups of apple cider to a boil. Reduce the heat and simmer (small bubbles around edges) until the cider reduces to about ¾ cup (this will take 8-10 minutes). Measure out 1/2 cup + 1 tablespoon of reduced apple cider. You should have approximately 3 tablespoons left. Set aside to cool. Don't wash the pan, as you'll use it for melting/browning the butter. Whisk Wet Ingredients: In a medium bowl, whisk together the ½ cup + 1 tablespoon of apple cider, sour cream, and vanilla extract until smooth. Set aside.
Brown the Butter: In the same medium sauce pan over medium-high heat, melt 8 tablespoons unsalted butter (reserve one tablespoon). As it melts, the butter will bubble, and then start to foam. Continue cooking, swirling the pan occasionally, until the butter turns golden brown and develops a nutty aroma. Be careful not to burn it—once it reaches a deep amber color, remove it from the heat immediately.Set aside to cool slightly. Whisk the Dry Ingredients: In a medium bowl, whisk together the flour, cornstarch, baking powder, baking soda, kosher salt, cinnamon, nutmeg, and cloves until well combined.
Whisk the Eggs & Sugar: In a large bowl, whisk the eggs and sugar together for about 2 minutes until the mixture is pale and frothy. While whisking continuously, slowly pour in the melted butter and keep whisking until the mixture is fully combined and smooth, with no traces of fat remaining. Set the saucepan aside.
Add the Dry to Wet: Gradually add the dry ingredients to the egg mixture in three parts, alternating with the reserved apple cider/sour cream mixture. Start and finish with the dry ingredients, whisking until the batter is smooth and free of lumps. The batter will be thin.
Bake: Pour the batter into the pan and place it on a rimmed baking sheet. Bake the cake, rotating halfway through, until it’s a deep golden brown and a tester inserted into the center comes out clean, about 65–75 minutes. Remove the pan from the oven and place it on a wire rack. Check the cake on the early side - the cake can take up to 80 minutes to bake depending on your oven. Brush with Apple Cider: While the cake is still hot, use a toothpick to poke holes all over the top of the cake. Brush or spoon 2 tablespoons of the reserved reduced cider over the cake, then let it cool for 10 minutes.
Brush Outside of Cake with Remaining Butter/Cider: Melt the remaining tablespoon of unsalted butter in the reserved saucepan and stir in the remaining tablespoon of reduced cider.Lift the cake onto a wire rack using the parchment paper and place the rack inside a rimmed baking sheet. Peel the parchment from the sides of the cake. Brush the warm butter-cider mixture over the top and sides of the cake. Generously coat the cake with cinnamon-sugar, rotating it with the parchment to catch any excess. Let the cake cool completely before slicing.