In large saucepot, melt butter over medium-low heat. Add garlic, carrots, celery, and onion, and cook 5 to 6 minutes or until vegetables are almost soft, stirring occasionally. Increase heat to medium; stir in 2 tablespoons flour. Gradually stir in broth.
Add potatoes and heat to simmering. Partially cover and simmer 15 minutes, stirring occasionally. In small bowl, whisk together milk and remaining 1 tablespoon flour; stir mixture into soup. Simmer 8 to 10 minutes or until soup thickens slightly, stirring