Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy using an electric mixer.

Beat in the eggs, one at a time, ensuring each is fully incorporated before adding the next. Mix in the freshly grated lemon zest, fresh lemon juice, and pure vanilla extract until the mixture is well combined. The lemon zest will give the cookies a delightful burst of flavor, so don't skimp on it!

In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed until a smooth dough forms. Gently fold in the poppy seeds, distributing them evenly throughout the dough.

Divide the dough in half. On a lightly floured surface, shape each half into a log about 2 inches in diameter. Roll the logs in parchment paper or plastic wrap and chill in the refrigerator for at least 2 hours. Chilling the dough will make it easier to slice later.

Once the dough has chilled, preheat your oven to 350°F (175°C) again. Remove the chilled logs from the refrigerator and slice them into approximately 1/4-inch thick rounds. Arrange the cookie rounds on the prepared baking sheet, leaving some space between them

Bake the cookies for 10-12 minutes or until the edges turn lightly golden. Be careful not to overbake, as these cookies taste best when they are soft and chewy. Let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.

If desired, prepare a simple glaze by mixing powdered sugar with fresh lemon juice until smooth. Drizzle the glaze over the cooled cookies and let it set before serving.