Place an oven rack in the centre of the oven. Preheat the oven to 160-170°C/gas 3. Butter and flour a 20cm by 20cm glass baking dish.
In a small bowl, combine the flour, thyme and salt. Set aside. Using a stand mixer fitted with the paddle attachment, beat together the butter and half of the icing sugar on high speed until light and fluffy, about 30 seconds. Beat in half of the lemon juice and the vanilla. Reduce the speed to low and gradually add the flour mixture.
Using damp fingers, press the dough into the prepared pan. Bake for 30 minutes until golden. Cool for 30 minutes.
In a medium bowl, whisk the remaining lemon juice and icing sugar together until smooth. Spoon the glaze over the cooled pastry base. Allow the glaze to harden, at room temperature, for at least 1 hour. Using a metal spatula, remove the pastry from the pan. Cut into 4cm square bars.
Arrange bars on a serving platter or store in an airtight plastic container at room temperature.