Melt butter in a large pot or Dutch oven over medium heat. Add onion, celery, and carrots. Cook until softened, about 8-10 minutes.
Stir in the flour and cook for 1 minute, stirring constantly.
Gradually whisk in the chicken broth until smooth. Bring to a simmer, stirring occasionally.
Stir in dry mustard, Worcestershire sauce, salt, and pepper. Reduce heat to low and simmer for 10 minutes, stirring occasionally.
In a separate bowl, combine the shredded cheeses.
Slowly whisk the milk into the soup.
Gradually add the shredded cheeses to the soup, a handful at a time, stirring until melted and smooth after each addition. Do not boil after adding cheese.
Stir in the beer. Heat gently until warmed through, about 5 minutes. Do not boil.
Taste and adjust seasoning if needed.
Serve hot, garnished with chives, pretzel bites, or croutons if desired.
Notes
For a smoother soup, you can blend it with an immersion blender or in batches in a regular blender before adding the cheese.
To make ahead, prepare the soup up to step 6. Cool completely, then refrigerate. Reheat gently over low heat, stirring frequently, before proceeding with steps 7-9.
Avoid boiling the soup after adding the cheese, as this can cause it to separate or become grainy.