Melt butter in a 3- or 4-quart soup pot over medium heat.

Add shallot and cook until translucent, 3 to 5 minutes.

Add carrot, celery, onion, potato, bay leaf, thyme, salt and pepper and stir to coat with butter.

Cook until celery and onion are translucent, 5 to 8 minutes.

Stir in flour and cook for 1 to 2 minutes, stirring constantly, until flour lightly browns.

Stir in dry mustard.

Add chicken stock and stir until liquid begins to thicken, about 1 minute.

Add beer and bring to a simmer, stirring occasionally, for 4 to 5 minutes.

Add milk and bring back to a simmer.

Continue simmering until vegetables are tender, about 5 minutes longer.

Take the soup from the heat and stir in cheddar, about 1/2 cup at a time, allowing the hot soup to melt the cheese.

Taste and adjust seasoning with salt and pepper. Garnish with fresh thyme and serve immediately.