Melt the butter in a small saucepan over low-medium heat, then whisk in flour and cook for about 1 minute, whisking often, to remove the raw flour taste. Whisk in beer, milk, dry mustard, Worcestershire sauce and a few grinds of black pepper. Bring to a simmer, whisking frequently, and cook until smooth, about 30 seconds more. Whisk in the shredded cheese, bring back to a simmer, and cook and whisk until very smooth and combined, about 1 more minute. Whisk in egg and cook for about 15 seconds more.