In a bowl, rub the lemon zest into the sugar until it feels fragrant and slightly damp. This brings out all the oils from the zest and infuses the sugar with lemon flavor.
Whisk in the melted butter until fully combined.
Add the egg, lemon juice, and vanilla extract. Mix until smooth and glossy.
Sift in the flour, cornstarch, baking powder, and salt. Fold gently until just combined. Be careful not to overmix, the dough should be soft but not sticky.
Scoop the dough using a large cookie scoop and place onto a tray or plate. Chill in the fridge for at least 15 minutes, or up to overnight.
Preheat your oven to 350°F (180°C).
Once chilled, roll the dough between your hands to smooth the edges, then gently press each one onto a lined baking sheet.
Bake for 9 to 11 minutes, just until the edges are set but the centers still look soft. Don’t overbake, they’ll continue to set on the baking tray
While the cookies are baking, prepare the cream cheese frosting. In a bowl, cream together the butter, cream cheese, icing sugar, and vanilla until smooth and fluffy. You can use a spatula or hand mixer, whichever you prefer. Transfer the frosting to a piping bag fitted with a round 2A tip, or just snip the end of the bag like I usually do.
Let the cookies cool on the baking tray for 10 minutes before transferring them to a wire rack to cool completely.
Once the cookies are fully cool, pipe the frosting on top. Finish with a little extra lemon zest if you’d like, totally optional but adds a lovely pop of color and flavor.