Add the oil and chicken to a large Dutch oven over medium heat. Sauté until the chicken is cooked through, about 5 minutes.
Add the butter, onions, and carrots; saute 3 - 4 minutes. Add garlic and saute for 30 seconds.
Add the chicken broth, potatoes, salt, and pepper. Bring to a soft boil over medium-high heat, then reduce to medium heat and cook 10 minutes.
Add broccoli and cook for another 5 minutes.
Whisk the flour, milk, and heavy cream; add to the Dutch oven and stir.
Turn the heat low and slowly add the cheese, stirring until completely dissolved.
Once the cheese dissolves, the soup is ready.
Serve and enjoy, friends!