Put the xylitol and butter in a large bowl and beat using an electric whisk until soft and fluffy, about 3-4 mins. Add the vanilla, lemon zest (if using), egg and a pinch of salt, then beat again to combine. Sift over the flour and fold it in using a spatula. Turn the dough out onto a sheet of baking parchment, and knead briefly to bring it together.

Shape the dough into a log and wrap up in the parchment. Chill for 40 mins. Heat the oven to 180C/160C fan/gas 6. Slice along the length of the log in 1cm intervals – you should get about 12 cookies. Arrange the cookies on baking tray lined with baking parchment, evenly spaced apart. Bake for 15-20 mins, or until lightly golden. Leave to cool on the tray for 5 mins, then transfer to a wire rack and leave to cool completely. Will keep in an airtight container for up to five days.