In a dutch oven or large saucepan cook onion, carrots, celery, and garlic in butter over medium-low heat. Stirring occasionally. Cook until vegetables begin to soften, about 5 minutes.

Reduce heat to low and sprinkle flour over vegetables. Cook, stirring occasionally for about 3 minutes. Add milk, broth, and beer in a stream, whisking as you add. Simmer, continuing to whisk occasionally, 5 minutes.

Add cubed potatoes, Worcestershire sauce, mustard, salt, and pepper. Cook for 15 minutes.

Add cheese about 1/4 cup at a time, stirring constantly. Cook until cheese is melted, 3 to 4 minutes (do not boil). Ladle into bowls and sprinkle with bacon.