Pre-heat the oven to 180°C / 160°C fan assisted oven / gas mark 4.
Add flour and cold butter to food processor. Switch on and process for about 10 seconds until the butter and flour have completely combined.
Add the sugar, eggs and vanilla extract into the food processor and combine until the dough comes together into a ball.
Tip out of the food processor onto a clean work surface and roll into a smooth ball.
Split the dough into quarters so you can roll out the dough in batches.
Take 2 large pieces of baking parchment and dust the bottom sheet with a little extra gluten-free flour. Place on of the cookie dough balls in the centre, flatten out slightly and dust over a little more flour. Place the second sheet of parchment on top and roll the dough out in between the parchment using a rolling pin to about 8mm.
Remove the top sheet of baking parchment and cut out the dough using your chosen cookie cutters. Remove the dough from around the cut out cookies, use a small palette knife to help lift up the cookies and place them on a lined baking sheet about 1 ½ inches apart.
Re-roll the pastry and cut out more biscuits, then repeat with the other dough balls until all the cookie dough has been cut out.
Chill the cut out cookies on their baking sheets in the fridge for 1 hour or in the freezer for 10 minutes.
Bake the cookies for 12 minutes until they are just starting to go very lightly brown at the edges.
Remove the cookies from the oven and allow to settle for 5 minutes, then remove the cookies from the tray and cool completely on a wire rack before icing.
Make the royal icing by sifting the icing sugar into a large mixing bowl (or stand mixer).
Pour the egg whites into the bowl and mix until the icing is thick, smooth and glossy. You want the consistency to be thick but so it just slowly pours off a teaspoon. You can add a little more icing sugar if it is not thick enough or add a few drops of warm water if it is too thick to drop off a teaspoon.
Split your icing into different bowls depending on how many colours you need and use food colouring to colour each little bowl of icing.
Fit small piping bags (or small ziplock bags) with piping nozzles (I used size 2) and fill the piping bags with the coloured icing. Snip off the end of the piping bag and pipe your cookies with the icing.
Allow the icing to fully set (it takes about 24 hours) before serving.