Melt butter on medium heat. Add onions and carrots. Saute until onions are clear. Add in flour and stir constantly about 2 minutes. Whisk in milk until smooth. Add in all the broth. Add desired amount of salt and pepper. Simmer about 15 minutes. Add broccoli, simmer about 10 minutes until softened. Use immersion blender to blend some of the chunks if desired. Add in potatoes, and let simmer until softened. Then add in cheese and stir until fully melted. Enjoy!