Heat up oil and butter in a soup pot over medium heat.
Place chicken in the pot, and cook until meat becomes opaque. Add in carrots and celery, continue cooking for 2-3 minutes. Blend in flour and give a good stir. Pour stock and let it boil. Add in broccoli and thyme, cook for another 3-5 minutes or until broccoli is al dente.
Lower heat and bring to a simmer, then add in cream and cheese. Stir lightly then turn off heat. Best served warm.