Melt 1/4 cup butter in a large stockpot over medium heat. Cook and stir celery and onion in butter until tender, 3 to 5 minutes. Pour chicken broth and water over the celery mixture; bring to a boil. Add cabbage, celery salt, oregano, thyme, garlic powder, salt, and black pepper to the pot. Cook soup until the cabbage is very tender, 45 to 60 minutes.
Melt 6 tablespoons butter in a skillet over medium heat. Stir 1 cup plus 1 tablespoon flour into melted butter until smooth.
Bring the soup to a rolling boil. Stir a small amount of the hot soup into flour mixture until smooth. Return all flour mixture to soup. Pour milk into the soup, reduce heat to medium-low, and bring soup to a simmer. Add cheese and stir until blended into a thick, creamy mixture. Thin by adding milk if needed.
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