Melt the butter in a large soup pot. Add onions, carrots, and celery and sauté over medium heat until tender about 4-5 minutes. Add garlic and cook 1 more minute until fragrant.
Add chicken broth and potatoes, bring to a boil, and cook until potatoes are tender, about 10 minutes. Mix flour with water, add, and simmer until soup is slightly thickened.