Preparation of Browned Butter: Begin by melting the butter in a medium frying pan over medium heat. Continue heating until the milk solids separate and acquire an amber color. Transfer the butter to a separate container, reserving 1 cup for the cookie dough and 2 tablespoons for the apple cider butter. Allow to cool completely.
Reduction of Apple Cider: Pour 1 cup of apple cider into a small saucepan and place over medium heat. Allow the cider to simmer for approximately 15 minutes or until it reduces to ¼ cup. Set aside to cool.
Sifting Dry Ingredients: In a medium mixing bowl, combine the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg. Sift together to ensure even distribution and set aside.
Combining Wet Ingredients: In a large mixing bowl, whisk together the cooled browned butter, reduced apple cider, brown sugar, granulated sugar, vanilla extract, egg, and apple sauce until the mixture is smooth and homogeneous.
Forming the Cookie Dough: Gradually fold the dry ingredients into the wet mixture using a rubber spatula, mixing until just combined to form a cohesive dough. Avoid over-mixing to ensure the cookies maintain a tender texture.
Preheating and Preparing Baking Sheets: Preheat the oven to 350°F (175°C). Line two cookie sheets with parchment paper.
Shaping the Cookies: Using a large cookie scoop, portion the dough into balls and arrange them on the prepared cookie sheets, allowing space for slight spreading.
Baking: Place one tray in the oven and bake for 13-15 minutes or until the cookies are just set. Repeat with the remaining tray. Allow the cookies to cool completely on a cooling rack before assembling.