Cream the butter with the sugar until just light and creamy in texture. Be careful not to overwork, or the cookies will spread during baking. Beat in the egg and vanilla extract until well combined. Add the flour and mix until it forms a dough. Gather into a ball, wrap in clingfilm and chill for at least 1 hour.
Preheat the oven to 190ºC/gas mark 5. Take half the dough, place on a floured surface and knead briefly. On a sheet of baking parchment, roll out the cookie dough to ½cm thick.
Draw a large D and A on to stiff card, cut out and use as templates. Place the templates on top of the dough and carefully cut out three letters to spell DAD. Remove any excess dough. Slide the cookies, still on the baking parchment, on to a baking tray and bake for 15 minutes, until golden brown at the edges. Repeat with the other half of the dough and any trimmings – you should get six large letters, ie two DADs.
Keep the cookies on the parchment paper and transfer to a wire rack to cool for a few minutes. Carefully slide off the paper.
Use the cookie letter templates to cut out corresponding shapes from the ready-rolled icing. Mix the icing sugar with a few drops of water to make a paste, then brush a little on to each biscuit before placing the icing on top. Decorate the iced cookies with sweets of your choice and the writing icing.