In a large pot, melt the butter over medium heat. Add the chopped onion and celery, seasoning with salt and pepper. Cook until the onion is soft and translucent, about 10 minutes.
Stir in the broth, bring the mixture to a boil, then reduce the heat and let it simmer for about 20 minutes, until the celery is tender.
Use an immersion blender to blend the soup until smooth and creamy. You can also blend in batches using a regular blender, then return to the pot.
Stir in the cream, then taste and adjust the seasoning as needed. Heat gently until warmed through, about 5 minutes. Serve hot.