Tip the gluten free flour into a food processor. Cut the lactose free butter into small pieces and drop them into the bowl, then whizz until the mixture looks like breadcrumbs.
Add the sugar, vanilla and egg yolks and whizz to a small dough. With your hands, roll the dough on a lightly floured surface into a sausage shape about 25cm/9in long and 5cm/2½in in diameter.
Wrap the roll and chill for at least 1 hour. (The roll can be frozen for up to 6 weeks. To use, remove from the freezer and allow to thaw for one hour at room temperature so that the dough is soft enough to be sliced into biscuits.)
Preheat the oven to 180C/gas 4/fan 160C and lightly grease 2 large baking sheets. Using a sharp knife, cut the dough into slices, each a generous 5mm/¼in thick, then arrange them on the greased baking sheets, spacing the biscuits slightly apart so they have a bit of room to spread as they cook.
Bake for 20 minutes until the biscuits are just turning pale golden around the edges, then transfer to a wire rack to cool. Dust generously with icing sugar. The biscuits will keep fresh for up to one week stored in an airtight tin.