Heat butter in a deep pot and add celery, onion, garlic, and thyme. Season well with salt and pepper.

Cook, stirring occasionally, until vegetables are soft, about 5 minutes.

Add the potato, carrot, stock, and milk to the pot and bring the mixture to a simmer.

Cover and cook for 20 minutes, stirring occasionally to keep the milk from forming a film, until the potato and carrot are cooked.

Purée the soup with an immersion blender or by transferring it to a food processor or blender.

Strain through a sieve, transfer back to the pot and heat before serving.

Adjust the seasoning and top with freshly ground black pepper powder and celery leaves.