In a stockpot, combine the broth, carrots, celery, onion and potatoes. Bring to a boil over medium-high heat; cover, reduce and simmer for 10 minutes or until the vegetables begin to become tender.
Add the broccoli; cover and simmer for 10 minutes.
Meanwhile, cook the bacon in a skillet over medium heat until crisp; remove from the pan and set aside. Drain the bacon fat and melt the butter in the same skillet. Once melted, whisk in the flour and cook for 1-2 minutes or until golden, stirring constantly.
Slowly whisk in the milk, 1 cup at a time, and cook for 5-7 minutes or until the mixture is bubbling and slightly thickened.
Stir in the shredded cheddar 1 cup at a time, stirring and melting the cheese completely before adding the next cup. Once melted, add the salt, pepper and dry mustard.
Slowly stir this cheese mixture into the soup pot, whisking to combine well. Add the cooked bacon and season to taste. If you want a thinner soup, simply add more milk or chicken broth.