Cook leeks, carrots, celery and garlic in butter in a 4-quart heavy saucepan over moderate heat, stirring occasionally, until vegetables begin to soften, about 5 minutes.
Reduce heat to moderately low and sprinkle flour over vegetables, then cook, stirring occasionally, 3 minutes.
Add milk, broth, and beer in a stream while whisking. Simmer, stirring occasionally for 10 minutes.
Stir in dry mustard, salt and pepper.
Add cheese, stir and cook until cheese is melted, 3 minutes (do not boil).
Blend with an immersion blender or a regular blender. Be careful when blending hot liquids in a regular blender, fill blender 1/2 way up and place a towel over the lid (hot liquids expand when blended).