STIR flour with baking powder and salt in a medium bowl. Add 2 tbsp lemon zest to flour mixture. Set aside.
BEAT butter with sugar in a large bowl, using an electric mixer on medium-high, until fluffy. Beat in egg. Gradually beat in flour mixture, just until combined. Gather into a ball.
POSITION racks in top and bottom thirds of oven. Preheat to 350F. Line 2 baking sheets with parchment.
ROLL into 1-in.-round balls and set on baking sheet. Make a deep indent in the centre of each ball. Bake in centre of oven until golden, 11 to 12 min. Let cookies cool on sheet for 1 min. Transfer to a rack to cool completely. Sift icing sugar over cookies. Fill cookies with 1/2 tsp lemon curd.