IN A 3-QUART HEAVY POT, preferably cast iron or copper, melt the butter over low heat, add the onions and cook, covered, for 15 minutes. Uncover and continue to cook until the onions turn a deep golden color, about 30 to 40 minutes, depending on your pot. Stir frequently. Add the broth and the nutmeg, cover and bring to a boil. Reduce heat and simmer for 15 minutes. Meanwhile, in a small pot, bring the beer to a boil over medium heat and boil until the liquid has reduced by half. Remove from the heat and add the Cheddar cheese, stirring until melted. Transfer this mixture to a blender. Add 1 cup of the onion soup and blend until smooth. Reserve. Remove the onion mixture from the heat and strain. Reserve the liquid.
Transfer the onions to a blender or food processor and puree until very smooth. Return the puree to the pot, add the reserved liquid and the Cheddar cheese mixture. Taste for salt and pepper. Serve piping hot in a tureen.