Preheat your oven to 350°F and line 2-3 baking sheets with parchment paper. While the oven heats, measure out all ingredients and bring your eggs to room temperature (about 70°F) if they aren't already—this helps them emulsify better with the butter and creates a smoother dough. Zest your lemons now and have everything ready before you start mixing.

In a medium bowl, whisk together the flour, baking powder, and salt. Set this mixture aside—you'll fold it into the wet ingredients later. This combines the leavening agent evenly throughout the flour, ensuring your cookies rise uniformly.

In a large bowl, beat together the soft butter, sugar, and lemon zest for 2-3 minutes until the mixture is pale and fluffy. This creaming process incorporates air into the dough, which helps the cookies rise and creates a tender crumb. I find that the lemon zest oils released during this step really intensify the lemon flavor throughout the entire cookie.

Add the room-temperature eggs, lemon juice, and vanilla to the butter mixture one at a time, beating well after each addition until fully incorporated. The room-temperature eggs emulsify smoothly with the butter rather than causing the mixture to look curdled. Beat until everything is well combined and the mixture looks homogenous.

Gently fold the dry ingredient mixture from Step 2 into the wet ingredients using a spatula or wooden spoon until just combined—don't overmix, as this can develop gluten and make cookies tough. Fold in the poppy seeds at the very end. The dough should come together without any visible streaks of flour.

Using a tablespoon, drop dough portions onto your prepared baking sheets, spacing them about 2 inches apart to allow for slight spreading. Bake for 12-14 minutes until the edges are set but the centers still look slightly underbaked—they'll continue cooking on the hot pan. Let cookies cool on the baking sheet for 2 minutes, then transfer them to a wire rack to cool completely before glazing. I like to give them a full 10 minutes on the rack to ensure the glaze sets properly.

While cookies cool, whisk together the sifted powdered sugar and lemon juice in a small bowl until smooth. Once the cookies are completely cool, dip the top of each cookie into the glaze, allowing excess to drip back into the bowl. Set the glazed cookies on a clean wire rack and let the glaze set for 15-20 minutes before serving or storing.