In a large stock pot, add shallots, celery and olive oil and cook over medium heat until the vegetables start to soften or the pan starts to brown (about 3 minutes).
Add chicken stalk, broccoli, potatoes, garlic powder, salt and pepper and boil until broccoli and potatoes are soft. (About 7-8 minutes).
While the potatoes and broccoli simmer, in a separate pan, heat butter over medium heat and when melted sprinkle the flour over and stir together making a roux.
Cook roux mixture for about 2 minutes then whisk in the milk.
Cook until thickened slightly then whisk in the cheese.
Once the cheese is melted and mixed into the roux and milk mixture.
Pour the milk and cheese mixture into the broccoli, potato and stock mixture and whisk until it’s all dissolved.
Bring to a boil and the soup should thicken slightly. (If you would like it thicker. Combine 2 tablespoons corn starch to 1/4 cup water and whisk in.) Taste the soup, add salt and pepper to taste.