Reduce the Apple Cider: Pour 1.5 cups pure apple cider into a small saucepan over medium heat. Simmer gently for 18 to 22 minutes until reduced to exactly 1/3 cup of thick, amber boiled cider syrup. Measure out 2 tablespoons of this syrup for the glaze and reserve the rest for the cookie dough. Allow to cool.

Brown the Butter: In a skillet over medium heat, melt the unsalted butter. Swirl constantly as it foams and crackles. After 4 to 5 minutes, golden-brown specks will appear and the aroma turns nutty and toasty. Immediately pour browned butter into a mixing bowl (scraping all browned bits) and let cool to room temperature for 15 minutes.

Mix Wet Ingredients: Whisk the cooled browned butter, dark brown sugar, and granulated sugar together until smooth. Whisk in the egg, egg yolk, vanilla extract, and cooled boiled cider reduction until completely creamy and cohesive.

Add Dry Ingredients: In a separate bowl, whisk together the flour, cream of tartar, baking soda, cinnamon, nutmeg, and salt. Fold the dry mixture into the wet bowl with a silicone spatula just until a soft, fragrant cookie dough forms. Chill the dough in the refrigerator for 30 minutes.

Roll and Bake: Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper. In a small bowl, combine 1/3 cup sugar and 1 tablespoon cinnamon. Scoop 2-tablespoon portions of dough, roll into smooth balls, and roll generously in the cinnamon sugar until completely coated. Place 2 inches apart on baking sheets. Bake for 10 to 11 minutes until the edges are set and tops crinkled, but the centers remain pillowy soft. Cool on sheet for 5 minutes, then transfer to a wire rack.

Glaze and Set: Whisk together powdered sugar, reserved boiled cider syrup, and milk until a silky glaze forms. Drizzle generously over the cooled cookies, allowing the glaze to pool into the crinkles. Let set for 10 minutes before serving!