1. Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
2. In a medium bowl, whisk together flour, baking powder, and salt.
3. In a large bowl, beat butter and granulated sugar until light and fluffy. Add egg, lemon zest, lemon juice, and vanilla, mixing well.
4. Gradually blend in dry ingredients until just combined.
5. Drop tablespoon-sized balls of dough onto prepared baking sheets.
6. Bake for 10-12 minutes, until edges are slightly golden. Cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
7. For the glaze, whisk together powdered sugar, lemon juice, zest, and salt. Drizzle over cooled cookies.
8. Let glaze set before serving.

Notes:

• For a stronger lemon flavor, add an extra tablespoon of lemon zest to the dough.
• Cookies can be stored in an airtight container at room temperature for up to a week.