Zest or finely grate the lemons into a bowl, add the double cream and vanilla seeds and gently whisk together.
Pour the mixture into a medium saucepan and heat slowly over a low heat to just below boiling, then add the caster sugar and dissolve.
Stir continuously over low-medium heat for 3 minutes, bringing slowly to the boil.
Take off the heat, place to one side and allow to cool (around 20 minutes).
Squeeze the lemons through a sieve into a bowl, then whisk in the cooled cream mixture.
Pour carefully into jam jars and seal (or use glasses) and place in the fridge to set.
To make the shortbread, tip the flour into a large mixing bowl, add in the butter and rub together until the mixture looks like fine breadcrumbs. Fold in the lavender sugar and the vanilla extract and work the mixture with your hands until it forms a ball.
Continue kneading the biscuit dough until it is smooth and the bowl sides are clean.
Wrap the dough in clingfilm and chill in the fridge for 30 minutes.
Preheat the oven to 130C Gas mark 1/2.
Remove the dough from the fridge and allow it to get to room temperature so it’s workable.
Lightly flour a work surface and roll out the dough until it is about 1cm thick, 24cm in length and 10cm wide.
Cut out rectangles about 3cm in width (this mixture should make 8 biscuits).
Transfer to a baking-parchment-lined baking tray.
Bake the shortbreads in the oven for 30 minutes until they are very pale gold in colour, remove to a wire rack and sprinkle with some lavender sugar whilst they are still warm.
Leave to cool before serving with the possets.