Melt the butter in a dutch oven or large pot.

Prepare and chop up your ingredients so that they are ready to add when you need them. Dice the potatoes into small pieces, dice the carrots, dice the onion, and mince the garlic. Chop the broccoli florets into small pieces.

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

Add the carrots and cook them 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. Continue to cook the soup to your desired thickness.

Salt to taste before serving.