This classic combination of melted cheese and toasted bread is also called Welsh rarebit — an attempt to dignify the original (and slightly silly) name. For best visual appeal, use an aged yellow Cheddar for the sauce.
Spread one side of bread slices with 2 tablespoons butter (total), then arrange slices, buttered sides up, on a baking sheet. Broil 4 to 6 inches from heat until golden brown, 1 to 4 minutes.
Melt remaining tablespoon butter in a 1-quart heavy saucepan over low heat, then add flour and cook, whisking constantly, 1 minute. Add beer and milk in a stream, whisking, then whisk in mustard, pepper, and cheese. Bring to a simmer over moderately low heat, whisking, then simmer, whisking, until smooth, about 2 minutes.
Remove from heat and immediately whisk in yolk. Serve cheese sauce on toast.
