1. In a large pot, melt the butter or heat the olive oil over medium heat.
2. Add the chopped onions and garlic. Sauté until the onions are translucent and the garlic is fragrant.
3. Add the chopped celery (including leaves) and diced potatoes to the pot. Cook for about 5-7 minutes, stirring occasionally.
4. Pour in the vegetable or chicken broth, ensuring that the vegetables are covered. Bring the mixture to a boil.
5. Reduce the heat to simmer and let it cook until the vegetables are tender (usually about 15-20 minutes).
6. Use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup to a blender in batches, blend, and then return it to the pot.
7. Pour in the milk or cream to the pureed soup, stirring well to combine. Adjust the consistency with more broth or milk if needed.
8. Season the soup with salt and pepper to taste. Adjust the seasoning as necessary.
9. Allow the soup to simmer for an additional 5-10 minutes to let the flavors meld.
10. Serve the celery soup hot, garnished with fresh herbs if desired.

Enjoy your homemade Celery Soup!