Stir chicken broth, carrots, onions, and black pepper together in a large saucepan over medium heat; bring to a simmer, reduce heat to medium-low, and cook until the carrots are tender, about 30 minutes.
Stir cheese spread, half-and-half, beer, milk, and Worcestershire sauce into the broth; cook, stirring frequently, until the cheese spread melts completely into the mixture, 5 to 7 minutes.
Whisk flour and butter together in a small bowl; stir into the mixture in the saucepan until smooth. Bring the liquid to a simmer, reduce heat to low, and cook, stirring frequently, until the soup is thickened, about 1 hour.
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