Melt the butter in a heavy saucepan over medium-low heat, and stir the Cheddar cheese and beer into the melted butter. Cook and stir until the cheese melts, about 5 minutes, and remove from the heat.
Whisk together the egg, salt, dry mustard, cayenne pepper, and Worcestershire sauce in a bowl. Gradually whisk the egg mixture into the cheese mixture, stirring between additions, until the egg mixture is thoroughly combined. Return the saucepan to the stove, and stir over low heat until the Welsh rabbit is hot and smooth.
