In a large pot, melt the butter over medium heat. Add the diced onion and cook until translucent, about 5 minutes.
Add the minced garlic and cook for another minute.
Sprinkle the flour over the onions and garlic, and stir to combine. Cook for 2 minutes, stirring constantly.
Slowly whisk in the beer, milk, and chicken broth. Bring to a simmer and cook for 10 minutes, stirring occasionally.
Reduce the heat to low and stir in the shredded cheddar cheese, a handful at a time, until melted and smooth.
Add the mustard powder and Worcestershire sauce. Season with salt and pepper to taste.
Simmer for another 5 minutes, stirring occasionally, until the soup is thickened and creamy.
Serve hot with crusty bread.