Preheat oven to 375°F/190°C. Line a baking sheet with parchment paper. In a medium bowl, whisk together flour, baking powder and salt. Set aside. In a mixer, combine butter and sugar until light and fluffy. Add egg and lemon extract, mixing until combined. Add flour mixture 1/2 cup/125 mL at a time until combined.
Roll dough into circles. Place on prepared baking sheet. Bake for 8-10 minutes. Remove from oven and let cool on rack.
Icing: In a small bowl, whisk together powdered sugar, milk and lemon extract until smooth. Add more milk to make thinner. Using a spoon, drizzle icing. Ready to serve when set.
Makes 24 cookies.