Prepare a hot water bain-marie (double boiler),  ready and be sure that you have a steady  64ºC (147ºF). 

Delicately add your 6 eggs (whole and intact), and cook them at this temperature for 1 hour. Use a  thermometer to be sure of the steady temperature.

In the meantime, clean your porcini. Sauté them in olive oil and butter for 5 to 6 minutes. 

Blend 2/3 of the porcini with chicken stock, heavy  cream, salt, and pepper, until you have a fine  purée. Reserve.

Bring milk, parmesan, ground black pepper and heavy cream to a simmer and mix with a hand-mixer, until it starts foaming. Reserve.

Warm 6 pasta bowls if you have some or 6 soup bowls work just fine.

Re­heat the mushroom purée, the leftover 1/3  of the porcini, and the parmesan foam, each  separately until warm.

Add a large spoon of purée, some sautéed porcini, and peel the eggs delicately, keep only the yolks.

Put the yolk on top of the purée, cover with a spoon of parmesan foam, a teaspoon of hazelnut oil, sprinkle a pinch of mushroom dust and enjoy immediately.