Combine all of the ingredients except for the heavy cream in a large soup pot. Bring to a boil, then cover and simmer for 35 minutes.
Using a hand-held immersion blender, puree the soup until silky smooth. (Alternatively, cool the soup slightly, then puree in a blender in batches, making sure to leave the hole in the lid open to allow the steam to escape.) Stir in the heavy cream and bring to a simmer. Taste and adjust seasoning (depending on the sweetness of the vegetables, you may need up to a tablespoon more sugar). Ladle the soup into bowls and garnish with croutons and thyme, if desired.
Freezer-Friendly Instructions: The soup can be frozen, without the cream, for up to 3 months. Defrost the soup in the refrigerator for 12 hours and then reheat it on the stovetop over medium heat until hot. Once heated through, add the cream and bring to a simmer before serving.
