Preheat your oven to 375°F and lightly grease two baking sheets. Set aside.
In a large bowl, cream together the unsalted butter and white sugar until the mixture is light and fluffy.
Add in the vanilla extract, lemon juice, lemon zest, and the egg. Beat until well incorporated.
In another bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and poppy seeds.
Slowly add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop the dough into 1½ inch balls and place on prepared baking sheets.
Bake for 9 to 11 minutes, until edges are lightly browned.
Make the icing by mixing the powdered sugar, lemon juice, milk, lemon zest, and vanilla extract until smooth.
Ice the cookies once cooled.
Garnish with lemon slices before serving.
