Melt butter in a large pot over medium heat. Add leeks and cook and stir until softened, about 5 minutes. Stir in celery; cook and stir until softened, about 5 minutes more. Add garlic; cook and stir until fragrant, about 1 minute. Stir in potatoes, vegetable broth, and water; bring to a boil. Reduce heat to medium-low and simmer until potatoes are tender and easily pierced with a fork, about 25 minutes.

Blend using an immersion blender or in a regular blender in batches. Stir in heavy cream until heated through. Season to taste with salt.