In a large pot over medium heat melt butter. Add onion & carrot. Saute for 2 minutes until softened. Add flour & stir for 3 minutes.
Stir in chicken broth, heavy cream, and seasonings, bring to a simmer. Add broccoli. Simmer for 10-15 minutes (until desired texture of broccoli is met) stirring continually.
Turn off heat. Add in cheese and stir until just melted. Taste and adjust seasonings if needed.
