In a large pot, melt the butter or heat the olive oil over medium heat.
Add the diced onion and chopped celery to the pot and sauté for about 5 minutes until they start to soften.
Add the diced potatoes and stir well to combine with the onions and celery.
Pour in the vegetable or chicken broth, making sure the ingredients are covered.
Bring the mixture to a boil, then reduce the heat to low and let it simmer for about 15-20 minutes, or until the potatoes are tender and easily pierced with a fork.
Use an immersion blender or a regular blender to puree the soup until smooth and creamy. Be careful when blending hot liquids.
Return the soup to the pot if you used a regular blender.
Stir in the milk or cream and season with salt and pepper to taste.
Heat the soup over low heat for a few more minutes until it's warmed through.
Ladle the Celery Potato Soup into bowls and garnish with fresh herbs if desired.
Serve hot and enjoy!You can also customize this basic recipe by adding other ingredients such as carrots, garlic, or herbs to enhance the flavor. Additionally, you can top the soup with grated cheese, croutons, or a drizzle of olive oil for extra texture and taste