Add the butter and oil to a pot over medium heat. Once the butter is melted, sauté the celery, garlic, and onion until soft, about 6-8 minutes.
Add the broth, chicken, and potatoes, season well with salt and pepper, bring to a simmer covered with a lid.
Simmer for about 30 minutes. Remove the chicken and pull it apart with 2 forks to shred. Then return it to the pot along with the corn.
Stir in the milk and cheese, bring to a simmer.
Dissolve the flour in an equal amount of water to form a paste. Add it to the simmering soup a little at a time until it becomes nice and thick. Taste and adjust the seasoning with salt if needed.
Garnish with celery leaves.