Peel the mushrooms and finely slice. Peel and halve the shallots and then dice finely. Remove the leaves of the thyme.
Preheat the oven to 220'C.
Sweat the shallots in hot olive oil with a pinch of salt. When they become transparent, add the mushrooms. Leave to sweat for a minute then add the thyme leaves and deglaze with the white wine. Once the white wine is absorbed, pour in the chicken stock and leave to simmer for about 20 minutes. Check on the seasoning, pour in the cream and leave to infuse on a medium heat.
Break the eggs in a bowl and add 100 ml vinegar (which will 'cook' the eggs), and leave aside. Bring a pan of water, with vinagar added, to the boil. Aim to keep the heat at 83'C. Stir ythe liquid and keep it in motion, add the eggs and then stop stirring. Poach the eggs for about 2/3 minutes and then take them out and rinse in cold water.
Place the ham on a baking tray and bake in the oven at 220'C for 6 minutes.
Pour the soup into bowls to serve, garnish with the egg and the cured ham 'crisps'.
«Do not poach the eggs for longer than 3 minutes.»