Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper or silicone baking mat.
In a medium bowl whisk together the flour, baking powder, cornstarch, and salt. Set aside.
Zest and juice 3 lemons; set aside. Mix 1 tablespoon of zest with 1 cup of sugar in a small bowl. Set aside.
In the bowl of a stand mixer, beat the butter, lemon sugar until light and fluffy, about 3 minutes. Beat in the egg, egg yolk, and honey. The add the lemon juice and poppy seeds and mix until combined. Gradually add in the flour mixture until just combined.
Divide the dough into 1 1/2 tablespoon-sized balls using <a href="https://amzn.to/3f0LGVg" target="_blank" rel="noreferrer noopener sponsored nofollow">cookie scoop</a> and drop onto prepared baking sheets, spacing about 2 inches apart. Gently flatten dough with your fingers or a spoon.
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 wire cooling racks to cool completely.
To make the glaze: In a small bowl combine the powdered sugar, lemon juice and lemon zest until a thick glaze forms. Add more sugar or juice as needed to get the glaze to the desired consistency. Dip each cookie into the glaze. Sprinkle with poppy seeds, if desired. Let the glaze set, about 20 minutes before eating or storing. Store the cookies in an airtight container at room temperature for up to 3 days.