Preheat your oven to 190˚C/375˚F/gas 5. Dust a clean surface and a rolling pin with flour and roll out the puff pastry until it's just over 0.5cm thick. Set aside.
Half the plums and pit them. Split a vanilla pod in half and scrape out the seeds with a knife. Alternatively you can use 1 tsp of vanilla.
Put the non-stick and ovenproof pan on medium heat and add the sugar, Kirsch, vanilla seeds and pod. Let the sugar dissolve and cook until the mixture forms a light caramel.
Once the caramel looks thick and sticky, add cubes of butter, stir to combine and cook for 1-2 minutes longer.
Carefully arrange your plum halves in caramel cut side down. (Keep the vanilla pod in, it will add much flavour and look gorgeous imprinted in your caramelised plums.)
Then quickly drape your puff pastry over the plums and tuck the sides in with a wooden spoon. Remember to not touch the pan or hot caramel with your hands or you will suffer bad burns. (I burned myself twice)
Bake the Tarte Tatin for 30 minutes, or until golden, with caramel bubbling around the edges.
Let it rest for 3-5 minutes.
Next step is to flip it over. Shake the pan lightly to make sure the tarte is still loose in the pan and the caramel hasn't gone hard. Put on oven mitts or cover your arm with a towel to prevent getting burned from hot caramel.
Put a large plate on top of your pan and quickly turn the pan over so the tarte ends up on the plate. (If you flipped the pan but the tarte didn't come out just shake it lightly until it falls out.)
Whip cream with sugar and lavender buds until stiff. Serve with hot Tarte Tatin.