Melt the butter in a large Dutch oven set over medium high heat. Saute the carrots, celery, and onion until soft and lightly browned, roughly 7 minutes, stirring occasionally. Add the garlic and cook until fragrant, stirring constantly.
Gradually sprinkle the flour on the veggies, stirring constantly over medium heat, and cook for 2 minutes.
Pour in the beer and bring it to a boil. Reduce heat and let it simmer for 20 minutes to soften the mirepoix.
While it is simmering, cook the bacon and blot off the excess grease. Allow to cool, then cut into ½ inch pieces. Set aside for the garnish.
Stir in the chicken broth, Worcestershire sauce, Dijon, and salt, then bring to a boil. Reduce heat and simmer for 10 minutes.
Remove the Dutch oven from the heat and let it cool for 5 minutes. Carefully pour the hot liquid, about 2 cups at a time, into a blender. Cover with lid, but leave the center hole open to let steam escape. As a safety precaution, cover the lid with an old towel and puree. Be careful with hot soup. Pour the pureed soup back into the Dutch oven, then repeat with the remaining soup.
Turn the heat to medium, and gradually whisk in the whole milk. Cook for 10 minutes, stirring occasionally, so it can thicken a little.
Remove the Dutch oven from the heat. Toss the freshly grated cheese with a little bit of cornstarch to prevent clumping. Gradually stir in the cheese until the cheese is melted and the soup is smooth. Add hot sauce and white pepper. Taste and adjust seasonings if necessary.
Garnish with the bacon pieces, chives, and a dollop of sour cream. Serve steaming hot or while it's still warm with our soft German pretzel buns.