Place a saucepan over medium heat.
Add the butter to the saucepan and allow it to melt completely.
Add the all-purpose flour to the melted butter.
Whisk continuously for approximately 2 minutes, or until the mixture is smooth and lightly cooked.
Gradually add the milk while whisking constantly.
Add the beer slowly, continuing to whisk until the mixture is smooth and free of lumps.
Bring the mixture to a gentle boil.
Continue cooking for 5 to 7 minutes, stirring frequently, until the sauce thickens.
Reduce the heat to low.
Add the grated cheddar cheese.
Stir until the cheese is fully melted and the sauce is smooth.
Add the grainy mustard, dried oregano, black pepper, and cayenne pepper.
Stir until the seasonings are evenly incorporated.
Taste the sauce and add salt or Tabasco sauce, if desired.
Remove the saucepan from the heat.
Transfer the cheese sauce to a serving bowl.
Sprinkle the top with additional cayenne pepper, if desired.
Serve warm with pretzels or other preferred dippers.