Put the dried porcini into a bowl and cover with just-boiled water. Rest for 10 minutes to rehydrate.
Meanwhile, finely chop the onion and garlic. Peel and dice the parsnips.
Heat half of the oil in a saucepan over a low heat. Add the onion and sauté for 5 minutes. Add the garlic and two-thirds of the thyme. Stir for a minute.
Drain the porcini, reserving the soaking water and setting aside half of them.
Roughly chop the chestnut mushrooms.
Add both mushrooms (except the porcini you set aside) to the pan, pour in the vermouth, if used, and cook for 1 minute.
Add the parsnip pieces, stock and reserved mushroom water. Bring to the boil, then simmer for 10-15 minutes, until the parsnips are tender.
Heat the other half of the oil in a frying pan. Add the remaining porcini and thyme, then season with salt &pepper. Stir for 2-3 minutes.
Blend the soup with a hand-held blender until you get a smooth, velvety soup. Add more stock if it's too thick.
Ladle the soup into bowls, then top with the fried porcini. Serve with a drizzle of cream.