Melt butter in a large soup pot.  Add onion, garlic, and carrot and saute until softened and fragrant, 3-4 minutes.   Add flour and stir constantly for a minute or two.  

Slowly pour in broth while stirring/whisking (this prevents the flour from clumping) and then add milk, dijon, salt and pepper.  Bring mixture to a simmer and let cook for 3-4 minutes, gently stirring, to thicken.  Add broccoli and continue simmering until broccoli is soft and cooked through, 5-10 minutes or to your liking.  Turn heat to low and add cheese, stirring until melted and smooth.  Make sure to taste at this point and add more salt to taste before serving.  If desired (I usually do this) lightly run an immersion blender through the soup.  Don’t completely puree, but just blend about half way. You can also take about 1/3 of the soup and pulse it in the blender and then add it back in. 

Remove from heat, serve in bowls and top with additional cheese if desired.  Makes about 8 cups of soup.