Preheat a stock pot or any large pot over medium/high heat.
Add 2 tbs butter.
Once the butter is melted, add the onion, celery, carrots, and garlic. Cook for about 2 minutes.
Add flour in while stirring until it thickens.
Slowly add the broth while stirring as if you are making a gravy. This step helps thicken the soup a bit.
Add the water, broccoli, and salt and bring to a boil and then simmer until veggies are cooked.
Optional: You can remove about 4 cups and use an immersion blender or food processor to make the soup a bit thicker by blending it and then adding it back.
Add cheese and stir until it melts.
Serve with a crusty bread such as homemade sourdough.