If you don't have any cooked chicken on hand, you will need to begin by cooking and deboning chicken.
Melt the butter in a large pot over medium/high heat. Add the chopped onion, celery, and carrots. Stir, cover, and cook for approx. 10 minutes or until veggies are tender.
4 tablespoons butter (1/2 stick), 1 small onion, chopped, 1/2 cup celery, chopped, 1 - 2 cups carrots, peeled and chopped
Add the dry seasonings, stir, and cook for a minute.
1 teaspoon seasoned salt, 1/2 teaspoon garlic powder, 1/2 teaspoon black pepper, 1/2 teaspoon dried thyme, 1/2 teaspoon paprika
Add the potatoes and the chicken broth and bring it to a full boil. Cover the pot, simmer, and cook until the potatoes are tender. (We like to leave our potatoes just a tad crunchy, so I only cook them for 5 - 7 minutes - it adds more variety in textures.)
2 - 3 cups potatoes, peeled and diced, 4 cups chicken broth
In a separate bowl, slowly whisk the milk into the flour to make a roux. Add only a bit of milk at a time and whisk vigorously, to avoid having lumps.
2 cups milk, 6 tablespoons all-purpose flour (a little less than 1/2 cup)
When all the veggies are tender, gradually whisk the roux (milk and flour mixture) into the simmering soup, stirring continuously. Heat and allow the soup to thicken, but do not let it come to a full boil.
Once the soup has thickened, add the cooked and chopped chicken and the cheese. Stir, and give the cheese a minute to melt.
2 1/2 cups cooked and diced chicken, 1 cup shredded cheddar cheese or Velveeta
Add salt to taste, stir, and serve.
Cool, refrigerate, and reheat any leftovers.