Step 1

Stir chicken broth, carrot, celery, and onion together in a saucepan; bring to a boil, reduce heat to medium-low, place a cover on the saucepan, and simmer until vegetables are tender, 6 to 8 minutes.

Step 2

Whisk milk, flour, and pepper together in a small bowl; stream into the broth mixture while stirring. Cook until thickened and bubbling, about 5 minutes.

Step 3

Stir American cheese into the liquid; cook and stir until melted smoothly into the mixture, 2 to 3 minutes.