Melt butter in a large pot. Add onion, celery and carrots and cook until soft, about 5 minutes. Stir in flour; cook one minute, stirring often. Stir in broth.
Add potatoes and beer. Bring to a boil, reduce heat, cover and simmer 20 minutes or until potatoes are soft.
Transfer vegetables to a food processor or blender. Process until pureed. Return to pan; add cream, cayenne, and salt to taste. Reheat to a simmer. Add cheese, 1/2 cup at a time and stir until melted. Do not boil. Garnish with additional shredded cheese and if you wish, bacon bits and popcorn.
Some suggested beer and cheese pairings:
Fresh Mozzarella with Dark Lager. A wonderful contrast: In this case dark malts and sweet dairy flavors. Try Gordon Biersch MÃ¤rzen or for a lighter touch Heineken Dark.
Pepper Jack with Winter Warmer. A big, malty beer will stand up well to the hot peppers and Monterey Jack. Great in front of a roaring fire. Consider Deschutes Jubelale, Pyramid Snowcap Ale.
Smoked Gouda and Bock. Another beer for cool days, smooth yet with enough toastiness to take on the mild smokiness of the cheese. A perfect choice would be Gordon Biersch Blonde Bock.
Gruyere and Witbier. The spices of the Belgian White beer -- coriander, orange peels and other 'secret" choices -- should meld well with the earthy, nutty Gruyere. Try with the origianl Witbier: Hoegaarden.
Aged Cheddar and Porter or Stout. A big Stout or Porter, with lots of chocolate and black malts so that it hints of coffee, should be able handle the complexity of a well aged, sharp Cheddar. Try Deschutes Black Butte Porter, Alaskan Smoked Porter (WOW!) or the Irish classic: Guinness Stout.