Melt butter in a six-quart pot over medium heat.
Add carrots, shallots, and garlic, and cook until vegetables are soft, about three to five minutes. Add dry mustard and cayenne pepper.
Gradually add flour, stirring constantly to prevent lumps from forming. Cook for another two minutes to get rid of the raw flour flavor.
Reduce heat to medium–low and add vegetable broth, beer, half-and-half, and milk. Cook for 15 minutes, stirring frequently.
Add cheeses one cup at a time, stirring constantly until cheese melts before adding the next cup.
Stir in Worcestershire and season to taste, with salt and white pepper.
Use an immersion blender to purée soup to a smooth, velvety texture.
Photography by Esti Waldman