Preheat oven to 160C/325F. Grease two oven trays; line with baking paper.
Beat butter, vanilla and sifted icing sugar in a small bowl with an electric mixer until light and fluffy. Transfer mixture to a large bowl; stir in sifted flour and arrowroot, in two batches.
With floured hands, roll rounded teaspoons of mixture into balls, then place 2.5cm (1 inch) apart on the trays. Flatten slightly with a floured fork into 3.5cm (1 1/2 inch) rounds.
Bake for 15 minutes or until a biscuit can be pushed gently without breaking. Stand on trays for 5 minutes; transfer to wire racks to cool.
Meanwhile make buttercream. Beat butter, sifted icing sugar and rind in a small bowl with an electric mixer until pale and fluffy; beat in juice.
Sandwich biscuits with buttercream. Dust with sifted icing sugar before serving, if you like.