Add unsalted butter to a Dutch oven or large heavy-based saucepan over medium heat. Once melted, add carrot, celery, onion, and garlic and sauté for 8-10 minutes until soft.
Add flour and stir until completely incorporated. Cook for 2-3 minutes.
Stir in the stock and increase heat to medium-high. Bring to a boil, and then reduce heat to medium-low. Simmer uncovered for approximately 30-35 minutes, stirring occasionally. Season with salt and pepper, to taste.
Remove from heat and blend the mixture with an immersion blender until smooth, if you have one. If not, transfer the liquid to a blender and blend until completely smooth. Work in batches if necessary.
Once smooth, return the mixture to the pot over medium-low heat.
Add the cream, goat cheese, and half the cheddar cheese. Stir continually until the cheese is completely melted. Add the remaining cheddar cheese and stir until melted.
Add the mustard, Worcestershire sauce, and beer and stir until blended. If the soup is too thick at this point, add a little additional stock.
Continuing simmering on medium-low heat for another 5-10 minutes, or until heated through.
Serve immediately with soft pretzel rolls or crusty bread of your choice.
Garnish with shredded cheddar cheese, red onion, and/or popcorn.
Notes
Take a “low and slow” approach while preparing this recipe. Most importantly, don’t allow the soup to boil after adding the cheese because it will cause it to separate.