Melt the butter in a saucepan over medium heat.
Add the chopped jalapeño and cook until softened.
Stir in the flour to the melted butter and jalapeños, combining well to form a roux.
Cook the mixture for about two minutes.
Slowly whisk in the milk and beer, ensuring the mixture stays smooth.
Allow it to thicken slightly as it heats.
Lower the heat and add the cream cheese, followed by the shredded cheddar cheese.
Stir until both cheeses are fully melted and the dip is smooth.
Season with dry mustard, salt, and pepper to your preferred taste.
Continue stirring until everything is well combined.
Serve immediately with your favorite dippers!