In large pot combine potatoes, carrots, garlic, chicken broth and just enough water to fully cover potatoes. Allow to simmer on medium heat for about 45 minutes or until carrots are fully cooked and potatoes are soft and mushy.
In a separate pan, mix milk and flour, and whisk with a fork until flour is fully incorporated. On medium heat, warm milk mixture. Stir constantly until mixture begins to thicken, then add both cheeses. Continue to stir constantly until cheeses are fully melted and has formed a sauce.
Mix cheese sauce with potato mixture and add steamed broccoli.
Serve with warm bread or tortilla chips.
Recipe by Clever Housewife at https://cleverhousewife.com/2013/11/combating-sickies-kleenex-creamy-broccoli-cheese-soup/