Preheat the oven to 350°F (180°C) and line a baking tray with parchment paper. Set aside.
Add the softened butter and white sugar to your mixer and cream them together until smooth.
Add the lemon extract and egg and mix them in.
Add the all purpose flour, cornstarch, baking soda and salt and stir in by hand (with a spoon, but just don't use an electric mixer for this part).
Add the lemon zest and mix into a big ball of cookie dough.
Break off pieces of the dough and roll them into balls. Aim to get 20 balls out of the batch. Place them evenly on a parchment lined baking tray. Flatten the balls with a fork or the base of a glass.
Bake for 12 minutes. For an even softer cookie bake for 10 minutes.
Allow to cool on the tray and when cool, mix up your lemon glaze.
Add the powdered sugar, lemon juice and lemon extract to a bowl and mix it into a glaze.
Drizzle over the cookies and leave them for a few minutes for the glaze to set.