In a large pot over medium high heat, melt butter. Add in onions, carrots, and broccoli. Cook to soften about 5 - 10 minutes.
Slowly add in broth, milk, and cream. Sprinkle with flour and add salt, pepper, and red pepper flakes. Continue stirring and heating over medium heat until thickened. This will take approx 10-15 minutes.
Once thick, add cheese and stir until melted and smooth. Serve and enjoy!
Recipe by The Gingham Apron at https://www.theginghamapron.com/broccoli-cheese-soup/