Put the butter into a large mixing bowl and use an electric whisk to beat it. Add the icing sugar, and mix that through, followed by the eggs, vanilla and salt. When the mixture is smooth, add the flour, give it a quick stir with a wooden spoon then use the electric whisk to mix it all through.
Turn the dough onto a floured worktop and bring it together with your hands. Divide it in two, and wrap one half in cling film to save for later. Divide the remaining half into 6 pieces, each slightly smaller than the first. Colour each piece a different colour by adding a few drops of food colouring gel and kneading it in with your hands. You want very vibrant colours so add more food colouring until this is achieved. Add a bit more flour if the dough starts to get sticky.
Dust the worktop with more flour. Starting with the smallest piece of dough, roll it out into a cigar shape 20cm long. Take the next biggest piece of dough, and use a rolling pin to roll it out to 20 cm long, and wide enough to wrap fully around the first piece. Wrap it around, and seal the seam by squeezing it together with your fingers - trim any bits that are too long.
Repeat with the rest of the coloured dough, until you have a long cylinder of 6 different coloured circles. Use a large kitchen knife to slice it in half right down the middle. Split the reserved plain cookie dough in half, and roll out each piece to 0.5cm thick, big enough to fully wrap one of the rainbow pieces (you don’t need to worry about wrapping the ends). Do this, taking care not to lose the shape. Repeat with the other rainbow strip, then wrap both in cling film and refrigerate for one hour.
Preheat the oven to 180C (160C fan). Take the cookie dough out of the freezer and remove the cling film. Carefully cut into 1.5cm slices - you should have a clear rainbow pattern on each one. Lay out on a baking sheet and bake for 15 - 20 minutes until cooked through. Allow them to cool on a wire rack before serving.