Put the potatoes in a large pot of salted water. Bring to a boil, then simmer for 20 minutes until the potatoes are tender.
Meanwhile, heat the olive oil in a pan, add the shallot, cook for 2 minutes, then the mushrooms, cook for 7 to 8 minutes, until golden, salt and pepper.
Put the potatoes in a bowl, then mash them, then add the milk and margarine, salt and pepper. Mix well. Pass it through a blender and then through a sieve to obtain a smooth consistency.
Prepare the sabayon. Put the yolks in a saucepan, add 2 cl of water per egg, salt and pepper. Heat over low heat while stirring. The preparation will begin to thicken, be careful that it does not turn into a scrambled egg, the heat must be low. Add a little grated truffle, mix, add the fresh cream, mix, keep warm.
Prepare the poached eggs. Bring a saucepan to a boil and pour in the vinegar. Crack an egg into a ramekin. Swirl the water in the pan with a spoon and slowly pour in the egg. The water should keep spinning. Turn off the heat and cook for 3 minutes. Collect the egg with a slotted spoon and place it on absorbent paper. Do the same with others.
Put the puree at the bottom of the plates, add the mushrooms, the poached egg, pour the sabayon, and finish with grated truffle or shavings. Serve immediately.