Preheat the oven to 170°C (325°F/Gas 3) and line a baking tray with baking paper. Put the butter and lavender sugar in a bowl and use electric beaters to beat well, until a little pale and the sugar has dissolved, about 30 seconds. Beat in the egg and vanilla. Add the flour and mix through with a wooden spoon. Keep the dough in the fridge or make the biscuits immediately.
Break off balls of dough the size of a rum ball, about 20 g (¾ oz) each. Roll them into smooth balls with your hands, then flatten them a bit. Place on the lined tray and press a lavender tip gently onto the top of each. Sprinkle with a little sugar and bake for about 10 minutes, until just set but still very pale (they will harden as they cool). Move them to a wire rack to cool.