Peel off any tough outer skins of the mushroom caps and throw them away, then slice the mushrooms finely. Heat a large saucepan over a medium heat and pour in a splash of olive oil. Add the onion, celery, garlic, parsley stalks, thyme leaves and mushrooms, place a lid on top and sweat gently until softened.
Spoon 4 tablespoons of mushrooms out of the pan and put to one side. Pour the stock into the pan and bring to the boil. Turn the heat down and simmer for 15 minutes. Season with salt and pepper, then whiz with a hand-held blender until smooth. Pour in the cream, bring just back to the boil, then turn off the heat.
Toast the slices of ciabatta in a hot griddle pan, then top with most of the reserved mushrooms and drizzle with olive oil. Spoon the soup into deep, individual bowls, garnish with the chopped parsley and remaining mushrooms, and serve with the ciabatta crostini.