In a saucepan, combine all ingredients except cream, cornflour, Parmesan and salt. Bring to a boil over high heat, then reduce heat and simmer 15-20 minutes.
Remove from heat and puree with a hand blender. Stir in the Parmesan until melted.
Stir the cornflour into the cream until dissolved. Add the soup, stirring. Reheat over medium heat until soup is thick. Season with salt and serve.