In a large bowl, rub the powdered sugar and lavender together with your fingertips for about 1 minute.
Add the soft butter, vanilla and salt. Stir until smooth, creamy and pale.
Add the flour and cornstarch and stir gently until a soft dough forms.
Shape the dough into a log about 2 inches (5 cm) wide and 8 inches (20 cm) long. Wrap in parchment paper.
Chill for at least 1 hour, until very firm.
Heat the oven to 325°F (160°C) and line a baking sheet with parchment. Slice the log into rounds about 1/3 inch (8 mm) thick and place 1 inch (2.5 cm) apart. Bake for 14 to 16 minutes, until the edges are pale golden.
Cool on the pan for 5 minutes, then move to a wire rack to cool completely.