Preheat oven to 350°F and line baking tray with parchment paper.
Combine flour, baking powder, and salt in a bowl.
Beat butter and sugar until light and fluffy.
Add egg and vanilla extract, then mix until smooth.
Gradually incorporate dry mixture into wet mixture to form dough.
Scoop dough portions onto tray and flatten slightly.
Bake for 9–10 minutes until edges set.
Cool cookies completely on rack.
Mix Greek yogurt, powdered sugar, and vanilla for frosting.
Spread frosting evenly over cooled cookies and serve.