For the cookies:
- 2 cups all purpose flour
- 1 teaspoon baking powder
- 1/4 teaspoon salt
- 1 tablespoon poppy seeds
- 1 stick unsalted butter, at room temperature
- 3/4 cup granulated sugar
- 1 large egg
- 1 1/2 teaspoons vanilla extract
- 2 teaspoons fresh lemon zest
For the icing:
- 1 tablespoon fresh lemon juice
- 2/3 cup powdered sugar
Preheat the oven to 350°F. Line large baking sheets with parchment paper or silicone baking mats.
In a medium bowl whisk together the flour, baking powder, salt, and poppy seeds.
In a large bowl, use an electric mixer on medium speed to beat the butter and sugar until well combined, 2 to 3 minutes. Add the egg, vanilla, and lemon zest and beat until combined. On low speed gradually add the flour mixture and beat until just combined.
Place a large sheet of parchment paper or plastic wrap on a work surface and turn the dough out. Place another sheet of parchment or plastic wrap on top of the dough and roll out into an even 1/4-inch thickness. Use cookie cutters to cut out desired shapes from the dough. Transfer the cut-outs to the prepared baking sheets.
Bake for 12 to 15 minutes, rotating the sheets halfway through, until the edges are just golden. Remove the sheets to wire cooling wracks and let cool for 5 minutes before removing the cookies to racks to cool completely.
To make the icing, stir together the lemon juice and sugar until smooth. Add more lemon juice to thin the icing and more sugar to thicken the icing to desired consistency. Spread over the cooled cookies.