In a dutch oven or large stockpot over medium-low heat, add the bacon and cook it until crispy, stirring occasionally for about 10 minutes. Take the bacon out, leaving the bacon grease.
Add the butter to the pot and let it melt, add the onion, carrot, and celery, stir to combine in the fat. Cook, stirring occasionally, until softened, 10 minutes.
Add the garlic and thyme, stir it in until fragrant, 30 seconds.
Add the flour and stir it in to coat the veggies. Let this cook for 2 minutes, stirring constantly.
Slowly stream in the beer while whisking so no lumps form.
Slowly stream in the chicken stock and heavy cream, whisking constantly.
Add the dijon mustard, Worcestershire sauce, salt, and cayenne pepper, stir to combine. Bring to a simmer and simmer for 10 minutes uncovered, stirring occasionally.
Take off the heat and add the cheese, stir it in until melted and combined.
Serve immediately with more cheese for garnish and the crispy bacon on top.