16 (1/3-inch-thick) diagonal baguette slices
3 tablespoons unsalted butter, softened
1 tablespoon all-purpose flour
1/2 cup porter or ale
1/4 cup whole milk
1 teaspoon dry mustard
1/8 teaspoon black pepper
6 oz extra-sharp Cheddar, coarsely grated (about 1 1/2 cups)
1 large egg yolk

Preheat broiler. 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.