Wash and chop your celery, onions, and potatoes. The celery for the soup should be cut into approximately half-inch pieces, the onions should be diced, and the potatoes cut into eighths. The extra half cup of celery that you'll set to the side should be diced into smaller pieces than the other two cups of celery.
In a dutch oven or soup pot, melt 1/4 cup of butter on medium heat. Add the celery and onions. Cook on medium heat for at least five minutes, careful not to let it burn. When they get fragrant and start to soften, add the garlic and potatoes. Stir for another 2 minutes.
Add the flour to the cooking vegetables, and mix for another minute.
Add 4 cups of vegetable broth, along with salt, pepper, and sugar. Stir. Bring to a boil, and let simmer for at least 20 minutes, or until you can easily push a fork through the pieces of potatoes.
While your soup is cooking, heat a splash of butter or oil in a pan. Add the reserved 1/2 cup of diced celery to the pan, and cook on low heat for at least ten minutes, or until it's soft and fragrant.
When the soup is ready, let it cool for at least five minutes. Then, transfer to a blender in small batches or use an immersion blender. Blend until smooth and chunks of vegetables are gone.
Add up to half a cup of milk (optional) as well as the extra celery to the soup. Stir well. Do a final taste test to see if you need more salt and pepper, then serve and enjoy!