Heat oven to 350°F and line two baking sheets with parchment.
Whisk flour, 1½ tsp cinnamon, baking powder, baking soda, and salt in a bowl.
Cream softened butter, ¾ cup sugar, and brown sugar until light and fluffy, about 2 minutes.
Beat in the beaten egg and vanilla until smooth.
Stir in dry ingredients just until a soft dough forms; do not overmix.
Chill dough 20 minutes to firm slightly for easier rolling.
Combine ¼ cup sugar with 1 tsp cinnamon in a small bowl; place powdered sugar in another bowl.
Scoop tablespoon-size portions, roll into balls, coat in cinnamon sugar, then heavily in powdered sugar.
Arrange 2 inches apart on sheets and bake 9–11 minutes, until puffed and crackled.
Cool 5 minutes on the sheet, then move cookies to a rack to finish cooling.