Start by creaming the butter with the powdered sugar. You can use a whisk, spatula or a hand-held beater for this.
Mix in the lemon juice and zest and vanilla extract and mix together.
Combine the flour and cornflour adding a ¼ cup at a time to the creamed butter and lemon mixture. Mix gently until all the flour has been combined into the creamed mixture.
Press and gather the dough lightly together and place it in a sheet of foil or cling wrap. Seal the wrap and place it in the refrigerator for 30 minutes or freezer for 15 minutes to chill. This will make it firmer and easier to roll and cut into shapes.
Roll the chilled dough between 2 sheets of wax or baking/ parchment paper. This ensures that the dough does not stick to the rolling pin. It also eliminates the need for the use of more flour, creating a softer bake.
Cut the cookies with a cutter dipped in flour. Arrange the cut cookies on a baking sheet and bake for between 15 and 18 minutes in a preheated oven of 350°F / 180°C.
It should just be lightly browned on the edges and still pale but baked on the inside. Leave on the baking tray for about 2 minutes before transferring to a cooling rack.
Sandwich the cooled cookies with lemon buttercream. Roll the cookies in powdered / icing sugar or just sift it over the sandwiched cookies.