Preheat the oven to 325F
In a bowl, whisk together the flour, poppy seeds, baking powder and salt. Set aside.
In the bowl of a standing mixer or with an electric mixer, cream together the butter and sugar until light and fluffy, about 3 minutes.
Add the egg and vanilla and beat until incorporated.
Slowly add the flour mixture to the wet mixture and mix until a dough forms.
Shape the dough into a disk and roll out to 1/4 inch thick. If the dough is too soft, place it in the refrigerator for 10-20 minutes.
Use cookie cutters to cut out desired shapes, and bake for 10-15 minutes, until the edges begin to turn golden brown.
In a small bowl, combine the powdered sugar and natural blue dye to make the icing. Allow cookies to cool completely before icing.