Melt butter in a stock pot over medium heat. Add the carrot, onion, and celery and sauté until softened but not browned.
Stir in the garlic and cook for two minutes more.
Add the flour and whisk for 3 minutes.
Add the ground mustard, salt and paprika and stir.
Pour in the beer and chicken broth and simmer for 10 minutes, stirring frequently.
Reduce the heat to medium low and use an immersion blender to get a smooth consistency.
Stir in the heavy cream and shredded cheese until well blended and cheese is melted.
Pour into bowl and top with pretzel bun croutons. Serve immediately.