Put the flour and ground rice in a mixing bowl or a food processor. Add the butter and rub in with your fingertips or process until the mixture resembles fine breadcrumbs.
Stir in the sugar and lavender petals and squeeze the crumbs together with your hands to form a smooth ball. Knead lightly then roll out on a lightly floured surface until 5 mm (¼ inch) thick. Stamp out 7.5 cm (3 inch) circles using a fluted round biscuit cutter. Transfer to an ungreased baking sheet. Reknead the trimmings and continue rolling and stamping out until you have made 16 biscuits.
Prick with a fork, bake in a preheated oven, 160°C (325°F), Gas Mark 3, for 10–12 minutes until pale golden. Leave to cool on the baking tray.
To serve, halve 4 of the smallest strawberries, hull and slice the rest. Whip the cream and spoon over 8 of the biscuits. Top with the sliced strawberries then the remaining biscuits. Spoon the remaining cream on top and decorate with the reserved halved strawberries and tiny sprigs of lavender, if liked. Dust lightly with sifted icing sugar. These are best eaten on the day they are filled, but the plain biscuits can be stored in an airtight tin for up to 3 days.