In a large saucepan over medium heat, stir together oil, onion and garlic. Cook until soft. Pour in chicken broth and beer then add salt and pepper. Simmer until tender, about 12 minutes. Remove from heat.
Meanwhile, heat butter in a large soup pot over medium-high heat. Stir in flour with a wire whisk; cook, stirring until the flour is light brown, about 3 or 4 minutes. Gradually stir in milk, whisking to prevent scorching, until thickened. Remove from heat, and gradually stir in cheese. Keep warm.
Stir beer mixture into cheese mixture. Bring to a simmer, and cook 10 minutes.
**Sausage can be added to soup for more texture and flavor**