Melt butter in a large soup pot. Add onions, carrots, and celery sautéing over medium heat. Add garlic and cook a bit longer. Add chicken broth and potatoes bringing to a boil. Cook until potatoes are tender. Mix flour with water, add, then simmer until soup is slightly thickened. Add milk and broccoli, cooking until broccoli is cooked and soup is heated through. Stir in cheese, allow it to melt. Serve.
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