In a large pot or dutch oven over medium-high heat, melt the butter. Saute the onion, celery and carrots for one minute.
Add in the broccoli and potatoes and cover with the chicken broth. Season with salt and pepper.
Bring to a boil and simmer for 5-7 minutes, until the potatoes are just tender. Meanwhile, mix together the milk and flour until well combined.
Add the milk and flour mixture to the pot, stirring until smooth. Bring the soup back to a boil and turn down to medium-low heat. Simmer the soup for 7-10 minutes until it has thickened.
Turn off the heat and add the cheese to the soup, stirring until blended. Serve hot.