2 tablespoons unsalted butter
2 tablespoons all purpose flour
1 teaspoon dry mustard powder
1 teaspoon Worcestershire sauce
½ cup dark beer, preferably porter
¾ cup whole milk
6 ounces aged cheddar cheese, grated
Kosher salt and freshly ground black pepper, to taste
8 slices country bread
Olive oil, for drizzling
In a medium saucepan over medium heat, melt the butter. Whisk in the flour and mustard powder and cook, whisking, for 30 seconds. Pour in the Worcestershire sauce and beer and whisk until smooth, then pour in the milk and whisk to combine. Add the cheese bit by bit, whisking until it melts into the sauce. Bring to a simmer, whisking, and simmer until the sauce is thick enough to coat the back of a spoon, about 2 minutes. Remove from the heat.
Preheat the broiler. Arrange the slices of bread on a rimmed baking sheet and drizzle each slice on both sides with olive oil. Set the baking sheet a few inches from the broiler and broil until the bread is toasted on the first side, then flip and broil on the second side until toasted. Arrange 2 slices of bread on each plate. Return the cheese sauce to low heat and whisk until smooth and hot. Spoon a generous amount of cheese sauce over the toasted bread slices and serve immediately.
Leftover cheese sauce can be cooled, then transferred to a lidded container and refrigerated. It can be reheated over low heat and spooned over toast as described above, or you can toast a slice of bread, spread the cold cheese sauce over the toast (it will have the texture of peanut butter when cold) and broil until browned and bubbly. Leftover cheese sauce is also delicious on a baked potato, spooned over cooked broccoli or spread, cold, on crackers.