Preheat oven to 150°C. Line a tray with baking paper and set aside.
Combine 200g softened butter and 60g icing sugar in the bowl or electric mixer and beat with the paddle attachment on high speed for 5 minutes. Keep mixing until the mixture is pale and light. Add the vanilla extract.
Sift in the flour, then beat on low to combine.
Scoop the mixture (using an ice-cream scoop) into balls. You should fit about 15-20 balls on a tray at a time. Avoid overcrowding.
Use a fork to press each ball down into a disc. Bake in the oven for 15-20 minutes or until the bottoms are very light golden brown.
Repeat with the remaining mixture. You want to have 40 pieces in total.
Allow to cool completely on a wire rack.
Use an electric mixer to beat the extra butter and icing sugar in a bowl until light and fluffy. Add the lemon zest and best to combined.
Spread the butter mixture over the flat side of half the biscuits and sandwich together with remaining biscuits.