Pour the apple cider into a small sauce pan. Heat the apple cider to a gentle boil or simmer over medium-high heat until it reduces down to ¼ cup (59 ml). This takes about 15 - 20 minutes; remove from heat and set aside to cool.
In another pot, melt butter over low heat until it begins to foam, stirring frequently until it smells nutty; cool slightly before transferring to a bowl.
Whisk together flour, baking powder, baking soda, cornstarch, spices, and salt in a separate bowl until combined.
Combine cooled brown butter with sugars in a mixing bowl; whisk in egg, yolk, cider, and vanilla until smooth.
Gradually stir dry ingredients into wet ingredients until just combined; let dough rest before preheating oven.
Scoop dough onto prepared baking sheet; bake at 375 F (190 C) until edges are set.
Cool on sheet briefly before transferring to wire rack; prepare toppings while they cool.
Brush cooled cookies with melted butter-cider mixture then coat with cinnamon-sugar blend.
Drizzle cookies with glaze made from powdered sugar, vanilla extract, and cider.