In a large pot or Dutch oven, melt the butter over medium heat.
Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux.
Gradually whisk in the chicken broth and beer until smooth. Bring to a simmer, stirring occasionally.
Reduce heat to low and stir in the milk. Do not boil.
Add the shredded cheeses a handful at a time, stirring until melted and smooth after each addition. Continue stirring until the soup is creamy and well combined.
Stir in salt, pepper, and Worcestershire sauce. Taste and adjust seasoning if needed.
Serve hot, garnished with fresh chives or croutons if desired.
Notes
This soup is delicious served with crusty bread for dipping.