In a bowl of an electric mixer fitted with a paddle attachment, add the butter and sugar. Beat at medium-high speed until light and fluffy, about 5 minutes.
First, add the whole egg to the creamed mixture with the motor running, and beat until combined. Scrape down the side of the bowl and beat again. Then add the egg yolk and beat until well combined.
Add the vanilla and lemon zest to the sugar and egg mixture and mix until just combined.
Sift together the flour and salt and add this to the biscuit mix at once. Mix on medium-low speed until just combined. Remove the dough from the bowl, cover in plastic wrap, and refrigerate for 40 minutes.
Preheat the oven to 160°C (320°F) and line two large baking trays with parchment paper.
Remove the dough from the fridge and roll it out to ½ cm ( ¼ inch) thickness on a floured surface using a rolling pin. Cut out the cookies using a cookie cutter, for this recipe I used a flower shape 7cm (3inch) diameter cutter.
Place the cookies onto a lined baking tray lined with parchment paper and bake in a preheated oven for 12 to 15 minutes or until light golden brown. Allow the cookies to cool on a cooling rack.
Lemon Frosting
In a bowl of an electric mixer fitted with a paddle attachment, add the butter and icing sugar. Beat at medium speed until the mixture looks like fine breadcrumbs.
Combine the milk and vanilla and add this to the icing mixture with the motor running at low speed. Once added increase the speed of the mixer and beat until light and fluffy. Scraping down the sides of the bowl often.
Add the lemon juice and zest to the frosting and beat again, until light and fluffy. Add the frosting to a prepared piping bag.
Separate the cookies into the bottom and top halves. Pipe a swirl of frosting into the center of all of the bottom half cookies. Place the top half cookie onto the frosting and press them together. Enjoy!