• Set a rack in the bottom-third of the oven and preheat to 350℉/177℃.

  Grease an 8-inch by 8-inch square baking pan, then line with parchment paper so that at least two of the sides leave an overhang (this will make the cake easier to remove).

Reduce the apple cider

• Add 32 fluid ounces apple cider to a medium sauce pot and bring to a boil. Lower the heat to a vigorous simmer and reduce the cider for 25 - 30 minutes, or until the liquid has reduced to 2 cups. Use a flexible heat-proof spatula to occasionally stir and scrape any residue from the sides.

  Note: Be careful when pouring the hot liquid into a measuring cup to check if it's reduced enough. Remove the pot from the stove and wait until it cools down slightly (about 30 seconds, or until the mixture is no longer spurting out bubbles) before carefully pouring it into the measuring cup.
• Once the liquid has reduced, remove ½ cup from the pot. Cool until lukewarm, but not hot. Whisk in 60 grams full-fat sour cream and set aside.
• Make the apple cider glaze: Meanwhile, continue simmering the rest of the apple cider until it reduces to about ⅓ cup and thickens enough to coat the back of a spoon, about 15 minutes.

  Season with a pinch of salt. Set aside to cool.
• Make the streusel: Mix 62 grams all-purpose flour, 106 grams dark brown sugar, ½ teaspoon ground cinnamon, ¼ teaspoon diamond-crystal kosher salt. Pour in the melted 57 grams unsalted butter and smush with your hands until the streusel feels moist throughout and small crumbs form. Chill in the fridge while you prepare the other ingredients.

Prep the apples

• Mix 1 teaspoon flour and 1 tablespoon of the apple cider glaze in a small bowl. Toss to coat with 5 ounces peeled and sliced apples.

  Note: If the glaze feels very thick and difficult to work with, you can reheat it in the microwave for about 10 seconds to loosen it up.

Make the cake

• Cream the butter and sugars: In the bowl of a stand mixer fixed with a paddle attachment, add 170 grams unsalted butter and 50 grams granulated white sugar and 53 grams dark brown sugar. Mix on medium speed until light, fluffy, and doubled in size, about 4 - 5 minutes.
• Reduce speed to low, then add 1 large egg and 1 tablespoon vanilla extract. Mix on medium speed for about 30 seconds - 1 minute until whipped and fluffy. The mixture will appear to curdle, but just keep mixing it, it should smooth out.
• On low speed, add ½ teaspoon diamond-crystal kosher salt (plus more for seasoning), 1 ½ teaspoons baking powder, ½ teaspoon baking soda, and 1 ½ teaspoons ground cinnamon.

  Alternate adding 188 grams all-purpose flour and the apple cider/sour cream mixture until everything is just barely combined. Turn the mixer off, then use a spatula to fold in any remaining dry bits. Fold the sliced apples into the batter until just combined.

Layer the cake

• Transfer batter to the prepared pan. Use an offset spatula to smooth batter in an even layer. Finally, top the cake with the streusel in an even layer.
• Bake in the oven for 30 - 35 minutes, or until a toothpick or knife inserted into the center of the cake comes out clean (or with just a few crumbs). Remove from the heat.
• Immediately drizzle 2 tablespoons of the glaze all over the top. Cool cake for 10 minutes, then carefully remove from the baking pan and transfer to a wire cooling rack. Cool completely before slicing and serving.

  Note: If the glaze feels very thick and difficult to work with, you can reheat it in the microwave for about 10 seconds to loosen it up.