In a large pot combine chicken broth, carrots, potatoes, garlic and onion. Bring to a boil. Cover and simmer for about 10 minutes.
Add broccoli, cover and simmer for an additional 10 minutes.
While simmering, melt butter in a large sauce pan. Whisk in the flour and cook for another minute (until golden brown). Whisk in milk and cook for an additional 5 minutes until the sauce thickens
Add cheese and stir until it is all melted. Add salt. Pour cheese sauce into the soup and stir until well combined.
Add more milk for a thinner consistency and add any additional salt and pepper if needed.
Top with bacon and green onion.
