Place the plain flour, coconut flour, icing sugar, salt and butter in a food processor and blitz until it resembles sand. With the motor running, gradually add the ice water until it comes together into a ball. Shape the pastry into a disc, wrap in clingfilm and chill in the fridge for at least an hour.
Roll out the chilled pastry thinly on a lightly floured surface and use to line a 25cm tart tin, trim off the excess, prick the base with a fork and place the pastry case in the freezer for 15 minutes while you pre-heat the oven to 180C/350F/gas mark 4.
Line the tart case with greaseproof paper or a double layer of good quality clingfilm, going right into the corners, edges and up the sides then fill with baking beans or dried rice making sure that the sides are propped up.
Bake for about 25 minutes then remove the paper and beans, reduce the oven temperature to 170C/325F/gas mark 3 and return the tart case to the oven for about 15 minutes more, or until golden and crisp. If the edges start to colour before the middle is done then you can cover them with strips of tin foil.
Remove from the oven and leave to cool for 10 minutes then remove the tart case from the tin, transfer to a wire rack and leave to cool completely. If you are making the case the day before serving the tart then keep in an airtight container once cool.