In a stockpot over medium-low heat, melt the butter. Add the onion, celery and carrots and cook, stirring occasionally, until very soft, 10 to 15 minutes. Stir in the flour and cook for 3 to 5 minutes. Increase the heat to medium-high and whisk in the milk and stock. Bring to a simmer and cook, stirring often, until thickened, about 10 minutes.

Using an immersion blender, puree the soup until smooth. Strain the mixture through a fine-mesh sieve into a large bowl.

Return the mixture to the pot and set over medium heat. Add the ale, Worcestershire and mustard and simmer for 5 minutes. Whisk in the cheese 1D2 cup at a time, letting each addition melt before adding more; do not allow the soup to boil. Season with salt and cayenne.

Ladle the soup into warmed bowls and serve immediately. Serves 4 to 6.