Melt butter in a stockpot over medium-high heat. Add leeks and celery; cook and stir until softened, 3 to 5 minutes.
Add broth, potatoes, carrots, salt, and bay leaf; bring to a boil. Cook until potatoes and carrots are soft, about 20 minutes. Remove and discard bay leaf.
Blend soup with an immersion blender until smooth. Stir cream into blended soup. Reduce the heat to medium-low and simmer until thickened, about 20 minutes.