Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Whisk the flour, poppy seeds, baking soda and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 4 minutes. Add the egg, vanilla and 1 tablespoon lemon zest and beat until combined. Reduce the mixer speed to low; beat in the flour mixture, then increase the speed to medium high and beat until just combined.
Roll tablespoonfuls of dough into balls and arrange 2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are light golden and just set, 15 to 20 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.
Make the glaze: Whisk the confectioners' sugar, the remaining 1 teaspoon lemon zest and enough lemon juice to make a spreadable glaze. Spread on the cookies; sprinkle with nonpareils and let set, about 20 minutes.