Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

In a large bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the egg and lemon extract.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add to the wet ingredients, mixing until just combined.

Drop by rounded tablespoons onto the prepared baking sheets.

Bake for 8-10 minutes, or until the edges are lightly golden.

Let cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.

In a medium bowl, beat together the powdered sugar, softened butter, lemon juice, and lemon zest until smooth and creamy.

Frost the cooled cookies with the lemon frosting.