Melt the butter in a dutch oven or large pot

Prepare and chop up your ingredients so that they are ready to add. Dice the potatoes into small pieces (see the post images for size), dice the carrots, dice the onion, and mince the garlic. Chop the broccoli florets into small pieces.

Add the garlic and onion and cook over medium low heat for 7-10 minutes, or until the onion is softened 

Add the carrots and cook for 5 minutes over medium heat

Add the potatoes and vegetable broth and bring to a boil. Boil until the potatoes are tender and easily pierced with a fork

Mix together the milk and flour in a bowl, then add it to the vegetable soup

Add in the finely diced broccoli and simmer for 10-15 minutes

Add the cheese and stir until melted and the soup thickens. The soup will continue to thicken the longer that it cooks, and the potatoes will start to fall apart and become part of the soup. Continue to cook the soup to your desired thickness

Salt to taste before serving