In a large saucepan over medium heat, sauté the onion and celery in the butter until translucent but not browned, 3 to 4 minutes.
Add the fiddleheads, salt, and pepper and cook for 2 to 3 more minutes. Pick out 4 nice fiddleheads and set them aside to use as a garnish later.
Add the chicken broth and bring to boil, then reduce the heat and simmer the soup for 15 minutes, with the lid ajar on the saucepan.
Blend the soup in the saucepan with an immersion blender until creamy, or transfer it to a regular blender to purée (cover the lid of the blender with a tea towel and hold down the lid, as the soup will be hot and could cause the lid to pop off).
Add the cream and simmer the soup for an additional minute to reheat it.
Garnish each bowl with a reserved fiddlehead, and serve with chive toasts.