For sauce: In a saucepan, melt the butter over medium heat. Add the flour and cook, whisking constantly, for two minutes. Pour beer in slowly, stirring constantly, then whisk in salt, pepper, dry mustard, and Worcestershire sauce. Cook until mixture thickens slightly, about 3 minutes. Add cheese and continue cooking and stirring until mixture is smooth and bubbly, about 3 minutes. Remove from heat and serve over burgers.