Brown Butter. Cut the butter into 1 inch cubes. Melt in a skillet over medium heat, stirring or swirling gently to keep the butter moving. The butter will foam and bubble as the water boils away, then foam over the top as the milk fat particles begin to brown and turn fragrant. Remove to a heat-safe bowl, cover, and set aside to cool. You should have 182 grams of brown butter.

Reduce Apple Cider. Bring apple cider to a low boil, then reduce to a rapid simmer. Maintain the active simmer until the apple cider has reduced by half. You need 100 grams of reduced apple cider. Remove to a heat-safe bowl. Cover and place in the fridge along with the brown butter for approximately 1 hour.

Mise en Place. Bring brown butter, apple cider reduction, and eggs to room temperature (the butter should be cool, around 65°F, but soft to the touch). In one bowl, whisk together flour, baking powder, apple pie spices, and salt. Peel and dice fresh apple into another bowl. Whisk together cinnamon sugar topping. Grease an 8x4" loaf pan and line with a parchment paper sling. Set aside.

Preheat oven to 350°F.

Cream brown butter and sugar. Combine the brown butter and both sugars in the bowl of a stand mixer. Beat on low-medium speed until there's no loose sugar in the bowl, then increase speed to medium and continue creaming for 3-5 minutes, pausing to scrape down the bowl and the beater at least 3 times. Properly creamed, the butter and sugar will have a fluffy, airy, and paste-like texture and pale khaki color. Scrape down the sides of the bowl.

Add eggs. One at a time, crack each egg into a small bowl (to avoid getting shells in your cake!) then dump the egg into the mixer bowl, beating on medium speed for at least 60 seconds and scraping down the bowl again before adding the next egg. Scrape down the bowl again after the last egg has been added.

Alternate adding dry ingredients and apple cider. Add half the dry ingredients and mix on the lowest speed until almost combined. Scrape down the bowl and beater. Add the apple cider reduction and mix on low until combined, then stop and scrape the bowl and beater again. Add the remaining dry ingredients and mix on low speed until just a few streaks of flour remain. Do not over mix!

Add apples. Add the minced apples all at once and use a spatula to scrape down the sides of the bowl, folding the apples into the cake batter until evenly distributed and any remaining streaks of flour have been mixed in.

Bake. Scoop the batter into the parchment lined loaf pan. Use a mini offset spatula to smooth out the batter, pressing it down into the corners and sides of the pan so that there aren't any trapped air bubbles. Level off the top. Whisk together cinnamon sugar topping and sprinkle generously across the cake top, tilting the pan to get an even coating. Bake in the center of a 350°F oven for 60-65 minutes, until a toothpick inserted in the center comes out with just a few crumbs clinging to it.

Cool. Remove the pan to a cooling rack. Let cool 15-20 minutes, then use the parchment sling to lift the cake out of the pan to finish cooling completely before slicing.