Preheat oven to 350 degrees Fahrenheit.

Combine the flour, poppy seeds, baking powder, and salt in a bowl. In the bowl of an electric mixer fitted with the beater, cream margarine and sugar on medium-high speed until fluffy, then add egg and lemon extract. Reduce mixer speed to low and add dry ingredients; mix until just until combined. Stir in lemon zest.

Shape dough into walnut-sized balls (or smaller) and place them two inches apart on a parchment-lined baking sheet.

Bake for eight to 10 minutes. Remove from oven and transfer to cooling rack. Cool completely.

Combine all ingredients for icing and mix well. (You may need to adjust the amount of water, but the icing should be fairly thick.) Dip the top of each cookie into the icing. Place the cookies on a cooling rack to let excess icing drip off the sides (place waxed paper under rack on counter to minimize the mess). Let icing on cookies harden for at least half an hour.