Melt the butter in a medium saucepan over medium-high heat, then whisk in the flour. Whisk in the Dijon and season with some salt and pepper. Cook for 3 minutes, whisking continually.
Whisk in the Worcestershire, then the cream and beer; whisk out any lumps. Bring the mixture to a boil and cook out the alcohol, about 1 minute. Stir in the Cheddar and let melt. Keep stirring over medium-high heat until thickened, 4 to 5 minutes. Serve over the pumpernickel toast.