Using an electric mixer, beat soft unsalted butter, caster sugar and vanilla extract together in a bowl until pale and creamy. Add egg and mix well.
Sift 2 cups plain flour and baking powder over and fold in until combined. Knead lightly on a floured surface until smooth. Divide dough in half and flatten each into a disc. Wrap in plastic and chill in the fridge for 30 minutes.
Preheat oven to 180°c. Line 2 baking trays with baking paper.
Roll out one portion of dough on a lightly floured surface until 4mm thick. Using cookie cutters, cut out shapes and transfer to trays. Bake for 12-15 minutes until golden. Transfer to wire racks to cool. Repeat with other dough half to make 45 cookies.
Knead ready-made white icing on a clean surface dusted with sifted icing sugar until smooth and no longer sticky. Divide into portions and add drops of food colouring to colour, as desired. We did 5 portions (white, yellow, pink, blue and green). Work with one portion at a time and keep remaining coloured portions wrapped tightly in plastic to prevent drying out. Roll out 1 portion of coloured icing until about 3mm thick. Cut out shapes using the same cutters.
Lightly brush a biscuit with egg white and lay the icing on top smoothing gently. Continue with remaining biscuits and coloured icings. Decorate with dots and stripes as desired.
Note: stir butter and sugar until they are light and fluffy. the butter is "creamed" when it has almost doubled in mass and it has lightened to a yellowish-white color