Melt butter in a pot over medium heat. Add leeks and cook and stir until tender, about 5 minutes. Stir in celery and cook for 5 minutes more. Add garlic; cook and stir for 2 minutes. Stir in potatoes and vegetable broth; reduce heat and let simmer until potatoes are tender, about 25 minutes.
Blend using an immersion blender or in a regular blender in batches. Stir in heavy cream and salt.