Begin by prepping your ingredients. Dice the potatoes into small pieces, chop the carrots, finely dice the onion, and mince the garlic. Additionally, chop the broccoli florets into small pieces for even cooking.

In a Dutch oven or large pot, melt the 2 tablespoons of butter over medium heat.

Add the minced garlic and diced onion. Sauté them over medium-low heat for about 7-10 minutes, or until the onions are softened and translucent.

Stir in the diced carrots and allow them to cook for an additional 5 minutes, maintaining medium heat.

Introduce the diced potatoes and pour in the 32 oz of vegetable broth. Bring the mixture to a boil. Once boiling, reduce the heat and simmer until the potatoes are tender and easily pierced with a fork, about 15-20 minutes.

In a small bowl, mix the 2 cups of milk with the 2 tablespoons of flour until smooth. Add this mixture to the soup, stirring well.

Incorporate the 2 cups of finely diced broccoli florets into the soup. Let it simmer for 10-15 minutes, allowing the flavors to meld.

Finally, add the freshly grated 8 oz of yellow sharp cheddar cheese to the pot. Stir continuously until the cheese is completely melted and the soup thickens. The longer you cook the soup, the thicker it will become as the potatoes break down.

Taste and add salt as needed before serving.