Melt butter in a large pot over medium heat.
Add chopped onion and sauté until translucent.
Stir in minced garlic and cook for another minute.
Sprinkle flour over the mixture, stirring constantly for 2-3 minutes.
Gradually whisk in the chicken broth until smooth.
Pour in the beer and bring to a simmer.
Reduce heat and stir in the heavy cream and Dijon mustard.
Add shredded cheddar cheese, stirring until melted and creamy.
Season with salt and pepper to taste.
Serve hot, garnished with additional cheese if desired.