In a small mixing bowl, place the flour, salt, white pepper, and cayenne pepper; stir to combine; set aside. In a medium saucepan, place the chicken broth, carrots, and celery; stir to combine. Cover the saucepan. Bring the mixture to a boil over high heat; reduce the heat and simmer 10 minutes until the vegetables are tender. Remove from the heat; set aside.
In a 31/2-quart heavy-bottomed saucepan, heat the butter over medium heat. Place the onions in the saucepan; sautÃ© five minutes until translucent but not brown. Remove from the heat. Add the flour mixture; stir until blended, with no lumps remaining. Add the chicken broth mixture and milk; stir to combine. Place over medium heat; cook the mixture until thickened and just under boiling, stirring constantly. Do not allow the mixture to boil. Add the brown sugar, cheese, and beer; stir constantly until the cheese melts. Continue cooking to just under boiling, stirring continuously. Do not allow the soup to boil. Remove from the heat.
To serve, ladle the soup into soup cups or bowls. Float a few kernels of popped corn on each serving.
MAKES ABOUT SIX 1-CUP SERVINGS