In a Dutch oven over medium heat, cook bacon until crisp. Transfer to a paper towel-lined plate to drain, then crumble; set aside.
To the bacon fat, add the onions, carrots, and garlic. Cook over moderate heat, occasionally stirring until vegetables begin to soften, about 5 minutes. Add the flour and mix well. Cook, frequently stirring, for 2-3 minutes or until the flour turns golden brown.
Add milk, broth, and beer in a stream, whisking, then simmer, whisking occasionally, 5 minutes or until foam subsides. Stir in Worcestershire sauce, mustard, salt, and pepper.
Add cheese by handfuls, stirring constantly, but gently, and cook until cheese is melted, 3 to 4 minutes (do not boil). Stir in half of the crumbled bacon.
Ladle soup into bowls and top with remaining bacon. Garnish with French fried onions and sliced green onion, if desired. Serve with your favorite beer!
Notes
Add beer gradually, mixing after each addition.
Use grated or shredded cheese to allow for even and quick melting.
Do not add the cheese cold; it should be at room temperature. Sudden change in temperature causes coagulation and fat separation that forms into clumps and creates grease.
You don't want a stringy and curdled consistency, so add cheese last and gradually. Keep the temperature low, and do not let it reach boiling point.
Stir frequently but not vigorously. Excessive stirring will result in proteins to clump and the formation of lumps in your soup.
This soup can easily adapt to a vegetarian alternative by merely leaving out the bacon and replacing the chicken with vegetable broth.