Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.

In a medium bowl whisk together the flour, baking powder, cornstarch, and salt.

In the bowl of an electric mixer, beat the butter, sugar, and lemon zest until light and fluffy, about 3 minutes. Beat in the egg, egg yolk, and honey. Add the lemon juice and poppy seeds and mix until combined. On low speed, gradually add in the flour mixture until just combined.

Divide the dough into 1 1/2 tablespoon-sized balls using a spring-loaded scoop and drop onto prepared baking sheets, spacing 2 inches apart. Gently flatten dough with the smooth side of a spatula.

Bake for 12 to 14 minutes or until cookies are just set and slightly golden brown. Cool cookies on baking sheet for 2 minutes then transfer to cooking racks to cool completely.

In a small bowl combine the powdered sugar and lemon juice until a thick glaze forms. Add more sugar or juice as needed. Dip each cookie into the glaze. Sprinkle with more zest and poppy seeds, if desired. Let the glaze set, about 20 minutes.

Store the cookies in an airtight container at room temperature for up to 3 days.