Simmer 1.25 cups apple cider in a small saucepan until reduced to about 1/4 cup. Cool completely.
Heat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, baking powder, baking soda, salt, 1 1/2 tsp cinnamon, nutmeg, and cloves in a bowl.
Cream softened butter, granulated sugar, and brown sugar until light and fluffy, about 2 minutes.
Beat in the egg, vanilla, and the cooled cider reduction until smooth.
Add dry ingredients to the bowl. Mix just until no dry streaks remain.
Chill the dough 15 minutes to firm slightly for easier scooping.
Stir 1 tsp cinnamon and 1/4 cup sugar together in a small bowl for rolling.
Scoop 1 1/2-tbsp portions. Roll into balls and coat in the cinnamon sugar.
Arrange on sheets, spacing 2 inches apart. Bake 11–13 minutes, until edges are set.
Cool 5 minutes on the sheet, then move to a rack and cool completely.
Whisk powdered sugar with 2 tbsp cider until smooth. Adjust with a splash of cider if needed.
Drizzle glaze over cooled cookies. Let set before serving.