In a large pot, melt the butter and add the onion, celery, carrots and garlic. Cook, stirring often, for 3-4 minutes, until the veggies are slightly tender and the onions are translucent.
Add the chicken broth and potatoes. Bring the soup to a simmer and cook, partially covered, until the potatoes are tender, about 8-10 minutes.
In a liquid measuring cup, vigorously whisk the flour and milk together until smooth (or blend in a blender). Whisk the mixture into the soup, stirring quickly, and cook over medium heat for 3-4 minutes, until the soup begins to thicken slightly. Stir often to ensure the soup doesn’t burn.
Add the softened cream cheese to the soup in 1-inch pieces. Let the cream cheese sit in the soup and warm through completely before stirring until smooth.
Add the cooked chicken and heat through. Season with salt and pepper. Serve.
