2 Tablespoons butter

1/2 cup chopped onion

1 cup finely chopped carrot

1 celery stick, finely chopped (feel free to add more celery if you like celery; I don't, so I don't add much)

1 Tablespoon minced garlic

4 cups chicken broth (I usually use a mixture of low-sodium chicken broth and broth made with chicken soup base because it gives it such nice flavor)

2 large baking potatoes, peeled and chopped

1 Tablespoon flour

1/2 cup water

2/3 cup milk

2 cups chopped broccoli

2 heaping cups shredded cheddar cheese