Heat a large stock pot or Dutch oven over medium/high heat. Add butter. 

When the butter is melted, add the onion and ¼ teaspoon of salt to the pot and cook the onion for 3-4 minutes. 

Add the broccoli, garlic powder, and another ¼ teaspoon of salt to the pot and sauté for 2-3 additional minutes. 

Pour the broth into the pot and bring to a boil. 

Turn the heat to low and carefully remove 1 cup of the broth from the pot and set aside. 

Add the carrots, black pepper and the rest of the salt to the pot and stir. Let the ingredients simmer over low heat. 

Next, add the 1 cup of broth removed from the pot to a medium bowl and whisk the flour into the broth. The mixture will thicken quickly. 

Pour the thickened broth back into the pot and whisk all the ingredients together.

Add the milk to the pot and whisk. 

Turn heat to medium and let the soup simmer for 4-5 minutes. 

Remove from the heat and slowly add the shredded cheese to the pot. Consistently stir the cheese into the soup until it is completely incorporated. 

Let the soup simmer over low heat until it is thick and reaches desired temperature and consistency.