Melt the butter in a large pot; add all the vegetables except the squash. Season with salt and freshly ground white pepper, cook gently without colour until soft.
Add the squash and continue cooking until the squash starts to break down a little.
Pour in enough stock to just cover. Increase the heat and bring to a boil. Lower the heat and simmer until all are soft.
Pour the soup into a colander set over a bowl. Place the solids into a blender with enough of the liquid to allow the machine to work efficiently, blend until silky smooth, pouring in more liquid as needed.
Pass through a fine meshed sieve into a clean sauce pan.
Heat a frying pan, add a little butter and sauté the mushrooms with the shallots thyme, salt and pepper. Cook until the mushrooms are soft and fragrant. Put to one side and keep them warm.
Reheat the soup. Add the cream and a tablespoon of chilled sweet butter and stir until absorbed and the soup is hot.
Pour into serving bowls, add some mushrooms, hazelnuts, parsley and a drizzle of oil to each bowl and serve.