Heat butter and oil over medium-high heat in a Dutch oven or other soup pot.
Add the scallions. Reduce heat to medium-low and cook for 2-3 minutes or until the scallions wilt.
Add the garlic and celery leaves. Cook for 6-7 minutes or until leaves wilt and reduce in volume.
Add the potato and chicken broth. Bring to a boil.
Reduce heat to medium and simmer uncovered for 15-20 minutes or until potato and other vegetables are very tender.
Remove from heat and add the cream.
Puree with an immersion blender or in batches in a food processor.
Season to taste with salt and black pepper.
