Heat butter and olive oil in a large pot over medium high heat.
Add onion, carrots, and celery and cook for 5 minutes.
Add potatoes and chicken broth and bring to a simmer. Cook for 10-12 minutes, until veggies are soft.
Add the broccoli and simmer for another 3-4 minutes.
Whisk flour and milk together in a small bowl and pour into the soup. Stir to combine and continue to stir as soup thickens.
Stir in the cheese until melted. Add salt and pepper.