Preheat oven to 200C/400F. Grease two oven trays; line with baking paper.
Beat butter, sugar and egg in a small bowl with an electric mixer until light and fluffy. Beat in sifted dry ingredients until just combined.
Spoon mixture into a piping bag fitted with a 1cm (1/2-inch) fluted tube. Pipe 3cm (1 1/4 inch) rosettes about 3cm (1 1/4 inch) apart on trays. Bake for about 10 minutes; cool on trays.
Meanwhile, make vienna cream. Beat butter and vanilla in a small bowl with an electric mixer until as white as possible. In two batches, gradually beat in sifted icing sugar and milk until combined.
Sandwich biscuits with vienna cream.