Spread one side of bread slices with 2 Tbsp of butter, then arrange slices, buttered side up , on a baking sheet. Broil 4-6" from heat until golden brown, 1-4 minutes.
Melt remaining tablespoons butter in a 1 quart heavy sauce pan over low heat, then add flour and cook, whisking constantly, about 1 minute. Add beer and milk in a stream while whisking. Add mustard, pepper, and cheese. Whisk until smooth, about 2 minutes.
Remove from heat and immediately whisk in yolk. Serve cheese sauce on toast.