Pour 1 cup (240ml) of apple cider into a small saucepan over medium heat. Simmer for 15-20 minutes until reduced to exactly 2 tablespoons (30ml) of a dark, thick syrup. Cool completely in the refrigerator.

In a large mixing bowl, beat the softened butter, brown sugar, and white sugar on medium speed for 2 minutes until light and fluffy.

Mix in the cooled apple cider syrup, vanilla extract, and the egg yolk until fully incorporated.

Whisk together the flour, cream of tartar, baking soda, ground cinnamon, and salt. Gently fold into the wet mixture until no flour streaks remain. Chill the dough for 30 minutes.

Whisk together 3 tbsp granulated sugar and 1 tsp cinnamon. Scoop 1.5 tablespoon portions of dough, roll into balls, and toss generously in the cinnamon sugar mixture.

Place on a parchment-lined baking sheet and bake at 350°F (175°C) for 10-12 minutes. The edges should be lightly browned while the centers look puffy and slightly underbaked. Rest on the pan for 5 minutes, then move to a wire rack.

Whisk the powdered sugar, milk, and vanilla extract until smooth and thick. Once the cookies are completely cool, pipe a thick zigzag pattern over the top. Let set for 20 minutes before serving.