Cream the butter and sugar together in a large bowl or in the bowl of a stand mixer until light and fluffy. Add the egg and golden syrup and combine. Add all other ingredients and mix together on low speed until well combined.
Split dough in half and shape each half into a disc. Wrap in plastic wrap and chill in the freezer for 1 hour, or fridge for 2 hours. At this point, you can also put the dough in the freezer to use at a later date.
Once you are ready to bake the cookies, preheat the oven to 180°C/350°F. Remove the cookie dough discs from the fridge or freezer and unwrap. If using frozen dough, allow to thaw in the fridge for an hour or so.
Roll the dough out until it is about 3-4mm thick. If the dough is too hard to roll out, leave it sitting for 10 minutes or so and then try again. Using Christmas cookie cutters, or whatever shapes you want to, cut out the cookies and lay them on a lined baking tray. Re-roll any scraps of dough to make more cookies. Bake for 12-14 minutes, checking them at 12 minutes, until they are looking golden brown. They will harden slightly as they cool, but if you prefer a crispier cookie, bake them for a couple of minutes longer.
Allow to cool on the tray for 5 minutes, then transfer to a cooling rack. Allow to cool completely before decorating.
Whisk the egg white in a medium sized bowl (or using a stand mixer) until soft peaks form. Slowly add the sifted icing sugar until the icing reaches a smooth, pipeable consistency. Add milk 1 teaspoon at a time if it is too thick, or add more icing sugar if it is too thin.
Spoon the icing into a piping bag with a thin nozzle or into a sandwich size snaplock bag and snip the end off. Decorate the cookies as you desire!