In a large bowl, cream together the softened butter and sugar until light and fluffy. Add the egg, lemon juice, lemon zest, and vanilla extract, mixing until fully combined.

In a separate bowl, whisk together the flour, baking powder, salt, and poppy seeds. Gradually add the dry ingredients to the wet mixture, mixing just until a soft dough forms.

Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper. Scoop tablespoon-sized portions of dough and roll into balls. Place them on the baking sheet, spacing about 2 inches apart. Slightly flatten each ball. Bake for 10–12 minutes, or until the edges are just turning golden. Let cool on the sheet for 5 minutes, then transfer to a wire rack.

Once the cookies are completely cool, whisk together the powdered sugar and lemon juice to create the glaze. Drizzle over each cookie and top with extra lemon zest if desired. Let the glaze set before serving.