Preheat the oven to 200°C/180°C fan. Peel and quarter the potatoes, making sure they are all roughly the same size so they cook evenly. Place the potatoes in a pan of cold water, season with a little salt and bring to the boil. Turn the heat down to a simmer and allow to cook for 15-20 minutes or until soft. Drain the cooked potatoes and leave in the pan to steam dry for a few minutes.
Heat the cream and milk in a saucepan and bring to a gentle simmer over a medium heat. While the potatoes are still hot, push them through a mouli or potato ricer and then fold the cream mixture into the potatoes along with 125g of the butter.
Place a non-stick frying pan over a medium heat and add the remaining 25g of butter to the pan along with the shallot, mushrooms, drained Porcini, thyme leaves and season with a little salt and pepper. Fry until soft and then stir in the Dijon mustard, chopped chives and a good slug of white truffle oil (if using).
Place the potato purée in a piping bag and pipe the purée into the bottom of six glass ovenproof jars or ramekins, top with the mushroom mixture, crack an egg into each jar on top of the potato and mushroom mixture and drizzle over a tablespoon of double cream. Sprinkle with a little grated Parmesan.
Place the jars in an oven tray of simmering hot water and cook until the egg whites are set: this should take about 15-20 minutes. Carefully lift the jars out of the water. Garnish each jar with a sprinkle of chives and sea salt flakes and serve with toasted soldiers of sourdough.