Before you start. Line a baking sheet with parchment paper and set it aside.
Rub the lemon zest into the granulated sugar until it resembles wet sand and is very fragrant. Pour the sugar into a stand mixing bowl and add the butter and light brown sugar. Cream until light and fluffy, 3 minutes.
Mix in the egg, egg yolk, and vanilla extract until just combined.
Mix in the flour, poppy seeds, baking soda, baking powder, and salt until just combined.
Scoop the cookie dough with a medium (two-tablespoon) cookie scoop onto the prepared baking pan. You should have roughly 27 cookie dough balls. Chill the tray in the freezer for at least 3-4 hours, overnight is best!
When you are ready to bake, preheat the oven to 350 F/180 C.
Bake the frozen cookies spaced at least two inches apart for 9-11 minutes, or until the edges are lightly golden brown but the centers are still puffy and underbaked. Let the tray cool on a wire rack before decorating.
For the lemon glaze: Whisk together the powdered sugar and lemon juice until smooth. Drizzle over the tops of the cookies. Sprinkle with extra lemon zest and poppy seeds if desired.
For lemon sugar topping: Rub together the lemon zest and sugar. Straight out of the oven, sprinkle the sugar over the tops of the cookies and gently press it into the tops. You must do it right after baking or the sugar will just fall off!